The stance that this book takes is something along the lines of "Can science provide the key that will unlock all the secrets of existence?" (to paraphrase the dust jacket copy), which is a bit like asking "Can God create a rock so big that he can not lift it?", in that it is ultimately unanswerable, and is the "wrong question" in any case. Contrary to what one would expect by the subtitle of "The Scientific Basis for a Rational World", Davis seems determined to keep himself in a grey zone straddling the line between the camps on the "creator" question, and as one who is in the "Rationalist" side of that division, it comes across as making a muddle of almost everything in the interest of simply keeping the fundies strung along.
Davies does hit all the usual points ... how the "God" referred to by Einstein, Hawking, and others is more a metaphor for "the ordered universe" and not the "eat dead burned bodies and get veins in my teeth" Yahweh/Allah that most church-goers conjure up whenever the term is used ... and how the "God of the gaps" (where God is called upon as an explanation where science has not filled a particular "gap" in knowledge) keeps getting smaller and smaller as science answers more questions (not that this is a challenge to most Fundies, whose grasp of even basic scientific concepts is often pitiful!). But he never reaches that "Dawkins zone" where the whole notion of a creating deity is laughed off stage.
To his credit, he does come up with legitimate issues to base his "doubt in doubt" on, the fine-tuning of cosmological physical figures needed to support the Anthropic Principle (that the universe is the way it is because if it wasn't the way it is, we wouldn't be here trying to figure out the way it is) being a key element. Davis appears to not feel comfortable with the "Multiverse" model of "ultimate reality" (in that all possible universes come into existence and that only some tiny fraction of those are in a position to support sentient beings and thus be observed), and says that positing a Creator who happened to make this particular universe "fine tuned" for our particular type of carbon-based life (he had a factoid in here that I'd previously missed: dealing with how unlikely carbon is, as its formation requires a simultaneous collision of three high-speed helium nuclei, which for quantum reasons can only efficiently happen at very specific energy "resonances" in large stars) seems to him to be more plausible than positing the Multiverse's nearly infinite randomly-tuned universes.
Of course, the question does pop up about "what's God done recently?", if there was a fine-tuning deity at the start of the Universe, has he just sat back with a bottomless bucket of popcorn to watch the show unfold? After all, despite what the "faithful" (who will set up elaborate shrines where water is leaking out of cracked cement in a form that might bear some vague resemblance to a female figure) hold, there are very few, if any, instances where the basic laws of physics (set up by God, remember?) have been circumvented in what one might call a "miracle" indicating some divine intervention in the way things are chugging along in the Real World.
And, pretty much, "so it goes" ... Davies puts up "scientific verities" which he has doubts on, compares them with the "creator" model, and pretty much all down the line calls it a tie. I'm sure that these "God" books sell better than his "hard science" books because there are Fundies out there who will grab up anything to bolster their "imaginary friend" case (and having a popular science writer like Davies expressing his own reservations about reasonably well-accepted scientific theories will be flogged by the yahoos into some delusional "science loses out to God!!!" propaganda), but for those whose favorite sport isn't thumping bibles and burning heretics ... this is a pretty weak structure for a book!
However, The Mind of God is not a total bust (see the "carbon factoid" noted above), and if one went into it knowing that it was just going to meander along and not really "get anywhere", it would certainly be a pleasant enough read. The hardcover edition I picked up is out of print, but available "new" for about four bucks from the Amazon new/used vendors, and there's a paperback edition that's still out there, so you could find this at your local brick-and-mortar book store, were you so inclined.