Well, Hart has now published a long rant at the theocratic apologetics site FirstThings, which advertises itself as advancing "a religiously informed public philosophy for the ordering of society." Hart's piece stands as a sort of review of 50 Voices of Disbelief: Why We Are Atheists (surprise! surprise! he didn't like it), but it goes on to attack the "New Atheism" more generally, with particular attention to Richard Dawkins, Christopher Hitchens, and A.C. Grayling.
Much of the rant consists of an attempt to defend the hopeless Argument from Contingency. All things that we see are contingent: i.e., they might not have existed. Sure, there might be causal explanations for their existence, but if you trace those causes back far enough, you still come to something that (logically speaking) might not have existed, so eventually (it's claimed) you need to postulate something that "necessarily exists" in order to explain the whole shebang. This is God, or so the argument runs.
But for a start, even if God does exist he (logically) might not have. Turning this around, it's logically possible, even in a world where God exists, that he mightn't have existed. There's nothing self-contradictory about a description of a world with no omnipotent, omniscient, angry, wine-loving, shellfish-abominating being. (Note: by "world" here we don't mean "physical universe"; we mean the entirety of reality including whatever spooky, non-physical ontology it might have.) The concept "God", however exactly we define that concept, is not instantiated in the actual world as a matter of logical necessity any more than the concept "neoconservative wanker" is (the world just happens to contain a lot of neoconservative wankers; as far as logic is concerned, it might not have). Even if God happened to exist, it would still be logically possible that "God" is an uninstantiated concept.
Meanwhile, there's no reason at all to worry that it's logically possible that whatever things do happen to exist might not have, or that it's logically possible that different things might have existed. Sure, the world - including any spooky ontology it might involve - could (where "could" refers to logical possibility) have been different. So what? It's a brute fact, not something required by logic, that the world is as it happens to be. Who would ever think otherwise, unless in the grip of a religion? Even Hart ultimately distances himself from the argument, sensing its sad lack of legs. The Argument from Contingency gets nowhere, and it acquires whatever thin veneer of plausibility it might have only by relying covertly on archaic concepts of necessary being and the like.
Alas, you can have a concept, and attach to it the high falutin' formula "absolute actuality", but you do not thereby guarantee that the concept is instantiated in the real world. Thus, God would be just as contingent as anything else.
You'd think the numerous historical failures (including that of Goedel!) to get an ontological argument off the ground for more than a few confused seconds would provide enough warning as to why contingency arguments inevitably crash down in flames. If ontological arguments fail, you don't have a necessarily-actualised concept of God, but if you don't have that you don't a decent argument from contingency. The Argument from Contingency is parasitic on the Ontological Argument.
Ontological arguments always fail, once they are carefully picked apart, because you can't just take the concept of some sort of substantial, if spooky, thing that is imagined to have various specific properties - e.g. being omnipotent, loving wine, hating shellfish, ordering genocides, prying into people's bedrooms, and so on - then define the concept into being actualised. It doesn't work that way. Commenters at Dawkins' site are having a field day with Hart.