What Professor Leiter quite properly criticizes is a failure to cite check. Part of cite checking is doing precisely what Professor Leiter does in his comments: pointing out places in a work that require either support (which, as he notes, doesn't seem to exist) or a disclaimer that the statement is the writer's opinion. That is not the same thing as fact-checking, which involves not the support cited, but the facts underlying that support. Here's an example:
3,4'-dimethyl diazoamino benzene has a molecular weight of 287.24, melts at 391K, and is water-soluble.[note]
[note]CRC Handbook of Chemistry and Physics, 62d ed. (1981) at C-301.
A cite-check would correct the page number to C-264, correct the molecular weight to 225.30, and note that the source does not provide any data on solubility. A fact-check would go to another source and question the accuracy of the stated melting point. Some math will show that in this instance it is just transposed down a couple of lines on the page, but the point is that this is a different process.
OK, I've split that hair finely enough for today. Why? Because one of the two errors could form the basis for a defamation claim, and the other could not. An article that is properly cite-checked, within "reasonability" standards, does nothing for or against a defamation claim except perhaps help a jury believe that there was no intent and thus reduce damages. Attempting to confirm the truthfulness of factual statements, though, does, at least when done competently. The book review Professor Leiter excoriates did neither; but proper cite-checking (which, as noted above, is more than just checking page numbers) would have pointed to the underlying problems. As he notes, "A footnote adducing the empirical evidence on behalf of [intelligent design] would have been welcome, but there is none to be found, and for an obvious reason: none exists."
Perhaps some of my urge to split hairs here comes from the different perspectives and vocabularies in the publishing industry and academia; in the end, perhaps it is only another example of how the publishing and entertainment industries thrive on doing things differently from everyone else.