The book is extremely light on knowledge of Christianity (Carrier only evinces a very rudimentary knowledge of C.S. Lewis’ brand of “mere Christianity”), and doesn’t even really attempt to touch the surface of theology and philosophy...
Slightly tangential, but Dawkins and Myers have taken to directly mocking the notion that a knowledge of these subjects is necessary to debunk theism. Their meta-argument is roughly that arguing the details of textile technology is nothing but a distraction from noticing that the emperor is stark naked. It dovetails nicely with their generally angry outlook, since it allows them to make various cracks about "discussing the merits of imported versus domestic newt tongues for making love potions," and such like.
I'd like to see a cogent meta-counter-argument explaining where "sophisticated theology" comes into play. As a non-theologian, I'm ill equipped to make it myself: I can see Myers and Dawkins et al veering off the beam, but can't necessarily articulate where they went wrong exactly. Unfortunately I can see that their mockery is partly on target: a sizable chunk of apology appears in my view also to rely fatally on the assumption of what they're trying to prove; they really do take the form of "discussing textiles" instead of confronting the question whether the emperor's posterior is or is not showing.
In "The God Delusion," which in all honesty I haven't read, I understand it to focus mainly on origins. God's reason for being is to explain the unexplainable concerning origins; we now have explanations for those previously unexplainable mysteries; therefore, there's no need for God. And since beings only exist if they're needed, God doesn't exist. QED. On that score my first reply is, "Jessica Simpson!" Clearly useless beings have an annoying habit of existing. So putting God out of a job does nothing to attack the question whether He exists or not.
Dawkins of course thinks he's addressing a deeper epistemological problem; he believes that the only reason people believe in God today is their need to fill the gaps. His error is clear: practically nobody believes in God for that reason. It's as good a theory as any other, I suppose, for how primeval people went about inventing their myths and superstitions, but subsequent generations don't repeat that process anew. They believe in God (or their parents' gods) for the simple reason that their parents did. It's now communicated to them, along with other cultural elements, as part of their upbringing. If asked why they believe, most will say they "Just do." So attacking "God of the gaps" doesn't lay a glove on them.
American fundamentalists (and their overseas brethren) make Dawkins overconfident, because they do retroactively pin their belief on such things. I.e., they didn't start believing in God to fill gaps, but after the fact they did start hanging their faith on the idea that these gaps are proofs of God. It makes their faith easy to destroy, because the foundations are so shaky: instead of attacking what might even be an impregnable structure, you undermine the foundations and watch it fall like Jericho. It has the opposite effect on those of us who aren't fundamentalists, because he's not touching our building nor its foundations, but he is strutting around proclaiming himself conqueror of all he surveys. It makes one want to snicker and call, "Jettez la vache!"
But to my regret, it's not a complete response to Dawkins. If I personally pointed this out to him, he would turn the tables and reply, "So tell me, Mr. Jeenyus, why do you believe in God?" Any reply I make will get me skewered, since my main reason is... I just do. I have only indirect evidence to point to, such as the power and meaning of scripture in my life, and mumble mumble prophecy. I'm not the David to send out to slay him with a well-chosen apologetic sling stone. So while I see that his theological unsophistication causes him to miss the mark, I'd be interested myself in a more complete, cogent explanation of what this mark is that he's missing.