To truly appreciate the facetiousness of Berlinski's arguments, one does well to view him in the context of actual opposition -- in a debate on evolutionary theory and its proposed alternatives. Here, Berlinski offers fallacious argument in full view of cameras and onlookers and apparently gets away with it.
He does it beautifully.
This is, of course, why I think it's worth examining: his pitch is attractive to consumers of educational policy argument, and we should give the pitch a review, better to appreciate what it does and does not offer.
When evolutionary proponents held forth certain recorded fossil observations as strong evidence of descent with modification by virtue of their apparent completeness, David Berlinski argued they were insufficient in light of gaps elsewhere in observed fossil specimens:
Barry Lynn: Mr. Berlinski, you're never going to be satisfied.This thesis regarding what one should expect evolution to predict in the fossil record underpins Berlinski's argument against evolution as an acceptable explanation for the observable evidence of speciation. When given an opportunity to interrogate opponents in a live debate, he offered this question as an intended show-stopper:
David Berlinski: You're right.
Lynn: Every time we find 16 new things, new fossils, to fill in the so-called fossil record that was missing, you just say, "Find 16 more."
Berlinski: I'll tell you exactly. Here is what Darwinian theory requires: for every significant morphological or physiological feature in a modern species we should have a panoply of intermediate forms that explains how they arrived. We don't have them for some good reasons, but we have nothing like an explanation ...
Berlinski: Would you agree, as almost everyone else affirms, that the overwhelming pattern of the fossil record is sharply discontinuous?While invoking the authority of the crowd he postulates agrees with him, he asks whether phenotypes observed among surviving fossils show the continuity he urges is required to support the theory he doubts. Why, however, should be urge phenotypic continuity as a necessary result of evolution?
Even assuming every fossil could or would be observed and recorded, why should anyone imagine phenotypic continuity in the fossil record? Lamarckian inheritance of acquired traits is not the theory under discussion. If one accepts that the mechanism by which ancestors pass traits to offspring is the transfer of genetic material, one would not expect continuity at all. One would expect discrete changes in phenotype to be acquired, associated with discrete changes in genetics. There are, after all, but four nucleic acids. Changes in a creature's inherited genetic structure must represent a discrete change, because the genetic mechanism affords only discrete changes and admits no half-measure: a point on a certain gene is either identical to that in its ancestor, or it is not. And there are only four molecules to fit in the spot in question. Given a mutation, though, the story isn't yet told to mere observers of form: the genetic change may manifest in a phenotypic change, or it may not.
Just to clarify a bit: Brown-haired parents who produce blonde descendants do not do so only by making several successive generations of progeny with increasingly lighter hair. They either have brown-haired children, or they have children who inherit recessive light-hair-encoding genes from both parents -- in which case the offspring's hair will appear sharply discontinuous from that of immediate ancestors. No one is ever surprised that Berlinski's continuous parade of intermediate forms do not appear when unexpected-looking children are born, even if traits cause one to doubt the identity of a child's father (spotting the mother at the time of birth is ordinarily trivial). The same is true if one child is tall and the other short: some kids are just thought to take after one parent's parent, or the like. What of it? Is anyone really surprised all visible changes between do not occur in the context of a continuous progression?
Yet, David Berlinski urges his audience to accept as a test of whether genetic evolution could explain observed speciation whether observed morphological changes among observed fossils are marked by continuity. This is absurd. In light of the discrete nature of the inheritance mechanism, it is in fact contrary to expectation. One would not expect continuity. One would expect isolated points of data -- where specimens were preserved for observation -- and one would expect these isolated points to be different.
And the phenotypic change -- the visible manifestation, if any, of a genetic change -- cannot be continuous if its mechanism is necessarily discrete.
However, discontinuity isn't the only argument Berlinski makes; he tries to make a pitch for unlikeliness, but instead reveals himself not to understand the basic mechanism by which inherited traits are thought to be passed to descendants. Later in the same debate, Berlinski has this exchange:
Berlinski: Let's turn to the question I so vainly tried to pump an answer from Dr. Scott ... How many morphological changes do think are required to effect the transition those charts of yours [depicting a series of fossils described as ancestors of modern whales] were said to document?Berlinski's idea that one should ask questions about morphological changes rather than genetic changes is also silly, unless he seeks to propose a different mechanism than genetics to explain the transmission of traits from ancestors to descendants. This, of course, hits on the fundamental weakness of David Berlinski's argument: he proposes nothing. He merely shrugs at whatever evidence is offered, and says "yes, but I'm not convinced."
Miller: I will give you a straight answer. And the straight answer is that when you look at two species that are separated by five million years --
Miller: -- of geological time the number of changes must be very, very large. However --
Berlinski: Give us a number.
Miller: -- However, recent studies of speciation -- and I'm sorry to pick this specific species, but it's relevant to your question -- in sunflowers have shown conclusively that a new species can be established in terms of a speciation-like isolation mechanism, with as few as ten genetic changes. That's your answer.
Berlinski: I've read the same Science papers you have but those are very close; a dog-like mammal and a whale are very far!
Miller: That's right! And the other end of the room is very far away, and it should not surprise you that I get there with one step at a time, and that's what we're talking.
Berlinski: No matter the number I give you, you will neither assent nor disagree with the number? If I say there are 100,00 morphological changes required to take a dog-like mammal living on the land to a whale --
Miller: Oh, sorry, yes, I will answer that. That's way too high .... The good genetic evidence is that there are about 100,000 genes in a human being. I would best guess there's somewhat fewer in whales. What you're telling me is that to change from one similar organism, an organism that looks more like a whale than any terrestrial animal that has ever lived, to a whale that looks more like a terrestrial animal than any whale has ever lived, would require every gene to change, and sir I --
Berlinski: No! I never talked about genes!
Miller: -- Sir, you asked me for a number and I said, on that basis, a hundred thousand is too high. 
What kind of test is that? He can keep saying he's unconvinced as long as doing so keeps him in speaking engagements.
And that's the beauty of his pitch. Calm and composed, Berlinski recites his demand for more evidence, only to shrug at whatever is produced. Faced with a fossil record documenting the transition from reptile ancestors to their mammal descendants -- so detailed the controversy is not whether it's the right lineage but where to decide observed fossils should start being labeled mammals -- he sidesteps by asking about the present state of knowledge of spiders' ancestors' fossils. Given an argument about genetics, he insists he never asked about genetics but is interested only in the evolution of phenotypic (he says "morphological") change. So long as he keeps his cool, his interrogators must perforce look like buffoons as they lose their composure in exasperation. Doesn't he know what he's talking about?
Well, apparently not -- but he'll look damned good while he does it. And he need neither propose a theory nor test one to do it.
Testing theories is, in fact, the real way to falsify (and thus correctly reject) them. To be sure, one might test theories in many ways; we are creative creatures and some interesting discoveries have been made using experiments composed of little more than logic. However, the applause-o-meter isn't the kind of test likely to produce consistent results of the sort on which one would want to base public policy. Trying to embarrass, confuse, exasperate, or misrepresent the views of opponents may be a good way to achieve notoriety and get appearance requests on entertainment programs, but it's not worthy of the name science.
If it weren't so easy to spot David Berlinski's rhetorical flaws, just imagine what his argument might support. So, thank God for bad rhetoric. It's a fantastic tip-off to the sort of reasoning that should be immediately discarded in the search for genuine data on which to base one's conclusions.
The most interesting thing about the debate over evolution is the fact that both sides accuse the other of politicizing the debate, and using power rather than evidence to "win" through policy implementation. The primacy of political power over actual data-supported research results isn't confined to evolution, either. We see this also in ecological policy, energy policy, health policy, liability policy -- the problems facing the quest to get good policy (in education, public health, trade, you name it) are beset by folks who care more about being thought right than actually making sure they're right -- people who care more about getting their intended result than getting the right result.
I strongly believe that a lively debate over scientific matters improves the likelihood that bad ideas will be weeded out before they become established as the basis for policies that will only consume resources without useful or intended results. Unfortunately, the sort of public spectacle Berlinski encourages with arguments about people's credentials, about the number of adherents to their point of view, about the number of papers that contain or don't contain the word "evolution" -- these are pure entertainment. They are vacuous of the reasoning one needed to inquire into the evidence about any theory about the world one might hope to test.
This is a serious problem, unfortunately. These entertainment-oriented "rhetorical" tools (argument ad hominem, appeal to authority, etc.) abound in political debates. Debates about scientific matters impacting public policy -- regarding the environment, public health, liability issues -- impact so many aspects of our lives that we should not stand still for analytical incompetence as the matters are deliberated (and supposedly reasoned). The result is that we -- consumers of policy produced by legislatures, employers, benefit plans, and judicial systems -- suffer from policy developed without the benefit of rational consideration.
Despite my strong conviction that ID offers no helpful thesis (if you teach kids "it's magic" it offers them no tool for understanding how to work with the forces -- still operating and yet remaining subject to discovery -- that operate upon and govern the world, and offers no opportunity to improve understanding and interaction with the world -- which in my view one of the fundamental reasons to acquire education), I would rather see legitimate efforts to hone good theories about speciation than merely see destruction by political force of folks whose principal crime is a crackpot theory. We have, on this planet, come to respect some crackpot theories over time (Galileo's theory of the orbit of the Earth about the Sun; Newton's theory that all matter tends to continue in motion until acted upon -- an idea that flew in the face of millennia of observation that things tend to come to a halt when no longer pushed; atomic theory; germ theory; the theory of sterile surgical technique; the dietary theory of the origin of pellagra; it's endless, isn't it?) and it's hard to know from the great sea of crackpot theories which ones will turn out to be supported by evidence once observer can be troubled to collect it. The ecological debate is like this much more than the ID debate, of course, as the ID debate plainly offers a naked theological proposition not subject to test, but my point is that we have to think about the standards by which we will regard theories (regardless of origin) when designing policy potentially impacted by the theories. At present we have in my view a simple political fight, and may be tolerable in the case in which the prevailing theory happens by blind chance to be more correct than its critics, but it's a poor model for consistently developing good policy, and worthless for developing ideal policy.
The most interesting thing about the debate over evolution is the fact that both sides accuse the other of politicizing the debate, and using power rather than evidence to "win" through policy implementation. The primacy of political power over actual data-supported research results isn't confined to evolution, either. In ecological policy, energy policy, health policy, liability policy -- the quest to get good policy (in education, public health, trade, liability, you name it) is beset by folks who care more about being thought right than they do about any activity designed to increase the chance of actually being right -- that is, people who care more about getting their intended result than getting the best available result.
What we need, perhaps, is to develop a general rule for deciding when a theory has sufficient evidence to support expending public resources on it. Any takers for this project?
 It's also possible, due to molecular folding issues, that single changes might alter molecular structure in such a way as to prohibit affected sections from being accessed by the molecular mechanisms that enable the creation of proteins that have significant impact in a developing organism. Assuming the mutation isn't fatal, code thus obsoleted might have a substantial and discontinuous impact on the phenotype of those expressing the traits involved. Obsoleted code might thereafter be subject to change or elimination in future generations without much observable impact -- except, of course, that the eliminated code might change macromolecular shapes by folding or other mechanisms in such a way as to alter the likelihood of other segments of the DNA will participate in the kinds of chemical interactions that lead to protein manufacture.
Thus, the right point change might create a folding issue that would have an enormous impact on the genetic material likely to be active in a developing organism. The expected result might be a big change, though it's highly likely such a change would be fatal if it resulted in phenotypic expression. If not, however, the possibility exists that the resultant change would be significant.
 In point of fact, since it's possible to have more than one point mutation in a gene, and that particular genes might be subject to repeated mutation over millions of years, I would tend to disagree with Miller that 100,000 is necessarily too high a number of mutations given his assumptions about the number of genes in the creatures at issue.
Modeling the number of mutations one would expect to be associated with a large speciation project spanning millions of years probably requires more considerable analysis than is plausible off the cuff during a live debate. Whether the number is enormous or not enormous doesn't really address the question of the possibility of descent with modification, it merely invites questions about the likelihood of a particular occurrence and the mechanisms by which different sorts of mutations might be possible.
There are some non-point-mutation sources of genetic alteration, like the so-called "jumping genes", that might be interesting to understand more about before trying to calculate the probability of speciation by descent with modification, or trying to use descent with modification to predict likely future fossil discovery patterns. For an entertaining (and scary) evening, read Doglas Preston's and Lincoln Child's purely-fictional horror-thriller Relic, the bogeyman of which originates with such a modification. While the monster is fictional, the discovery of "jumping genes" is not. A mechanism like the jumping gene might enable in one event to impart the accumulated effect of a whole geological age of mutation through the transposition, intact, of a proven gene from a different species with an evolutionary history as long as a gene's new host. Once isolated from its source species, the new gene would of course be subject to divergent evolution through the (slower and less radical) mechanism of random mutation.