Wieseltier's review has been critiqued by Brian Leiter (at Leiter Reports, here), P.Z. Myers (at Pharyngula, here), Taner Edis (at the Secular Outpost, here), and Michael Bains (at Silly Humans, here). I disagree with Bains about the term "scientism," even though I am quite sympathetic to "naturalized epistemology" and giving science a major role in philosophical questions. There is clearly quite a lot of room for disagreement about the idea that science should be the primary mechanism of inquiry in all domains--most scientists regularly argue that science draws no moral or ethical conclusions, which means they leave that area to philosophy or (a mistake, in my opinion) religion.
There is a key passage of Wieseltier's review that I partly agree with:
It will be plain that Dennett's approach to religion is contrived to evade religion's substance. He thinks that an inquiry into belief is made superfluous by an inquiry into the belief in belief. This is a very revealing mistake. You cannot disprove a belief unless you disprove its content. If you believe that you can disprove it any other way, by describing its origins or by describing its consequences, then you do not believe in reason.In general, the origin of a belief is irrelevant to its truth or falsity. However, if Dennett's mission is like Pascal Boyer's, to give an account of why people believe in religion in general, rather than to prove that religion is false, then this is not an objection to what Dennett is doing. Further, if the explanation produced is the best explanation around, then that is good reason to believe that explanation (over an explanation that says religion is divinely inspired).
The fact is that there are lots of different religious beliefs that people hold, and they contradict each other. We know from the outset that all religions cannot be true--in fact, the mere existence of the contradictions is sufficient to show that much of the content of most religions must be false. Why people continue to believe it is something that requires explanation.
If the best such explanation is a naturalistic one, and that explanation fits the evidence for all religious belief better than supernatural explanations, then that is good reason to favor the naturalistic explanation over the supernatural explanations.
Wieseltier seems to reject "inference to the best explanation" as a form of reason.
UPDATE: Dennett has responded with a letter to the New York Times, and Wieseltier responds immediately following.