The opening statements, 20 minutes each, are where I took notes, then I let the remaining three rounds (plus some questions at the end) play pretty much without interruption.
As usual, Dr. Craig cuts a striking, authoritative, confident figure, and delivers a clean and polished spiel, while Hitchens is more rumpled, given to occasionally backing up to make a point. I was surprised at how friendly and gracious Hitchens presented himself in the first round, and how generally well-behaved he was. Throughout the debate, Dr. Craig frames his arguments clearly, then stays within his framing, always stating his case as if it were true and obvious, even when he fails to provide evidence.
Dr. Craig cites five arguments for the existence of God - 1) the Cosmological argument (existence requires a creator); 2) the Teleological argument (design); 3) the argument from Moral authority; 4) the argument that Jesus' resurrection proves there is a god; 5) the argument from personal revelation. Hitchens does not refute these directly - in fact, neither did Sam Harris in his subsequent debate. I think I know why - these arguments seem tired and ineffective to those who have heard them before - but I can imagine that newbies will think "Why didn't Hitchens refute this? Dr. Craig must be right then."
The Cosmological Argument
I've gone over this one myself before. Dr. Craig does not provide any evidence that the universe requires a creator, or that a cause is required. In fact, the science is so new that claiming the universe is this way or that is not a certainty. Layering on claims that a cause is required, then proposing that it must be timeless, spaceless, unbelievably powerful, and "personal", is so contingent to be meaningless. As you see anywhere explanations are given, a simple one is preferred over more complex ones when there is no difference in explanatory power (Occam's Razor, don't ya know!) One demerit for Dr. Craig.
The Teleological Argument
Dr. Craig argues generally that the fine tuning of the universe points to the existence of a designer - citing some numbers presented by Barrow and Tipler in their 1986 book "The Anthropic Cosmological Principle" as a source that speaks to the improbability of the universe arising "by chance". Oddly, he goes to great lengths to criticize some of the main material at Barrow and Tipler on the Anthropic Principle vs. Divine Design - written no later than 2003, so I don't know if he truly believes these guys, or is cherry-picking. The argument from design seems to me a simple one. "We are pattern-seeking animals. We design, therefore we see design".
The Argument from Morality
This argument is the one that Sam Harris generally refutes in his book "The Moral Landscape" - so dwelling on this won't be enlightening. All books used as authority for religious doctrine claim moral authority, but using the Bible as an example, one can't look at each chapter and verse and discern an absolute and unambiguous set of moral principles that stand the test of time. Quite to the contrary, the Bible is full of contradictions and outright injunctions for immoral, even repugnant and murderous behavior. This points to anything but a just and loving God.
The Resurrection of Jesus
Resurrection being thrown in as an argument that supports the God hypothesis seems to be pandering to the religious audience. Dr. Craig claims the Resurrection as a fact, claims it was God's doing, and ignores the many lay explanations that can be made without special knowledge. Off the top of my head, I can imagine a bunch: 1) Jesus didn't die, and was "disappeared" by parties unknown; 2) Jesus did die, and his body was disappeared to eliminate it as a religious relic that could be used for future incitement of the faithful; 3) Jesus revived naturally and escaped; 4) common grave robbers; 5) the authors were wrong; 6) the authors had an ulterior motive; 7) the story changed from what the original authors documented. It might be noted in support of #3 that "resurrection from the dead" is still common today, and as recently as 1898 in England, several thousand recorded "rising from the dead" events occurred. People look dead. They wake up.
The argument from personal revelation is the weakest of all arguments for God. Just because we can imagine God, and think he touches us, is no reason to claim that as a cosmic proof that it exists. I suppose that in lay conversation, I might be inclined to go easy on a believer if they play this card - purely out of sympathy for my fellow man - but it was a surprising entry in this debate.
I thought Christopher held his own in the opening statements - but just as I thought Sam Harris missed his chance to nullify Craig's arguments, so did Hitchens. As the debate wore on, Craig remained organized and eloquent, whereas Hitchens, as anyone who watches him knows, refers to notes, fiddles with his glasses, appears to look down his nose at folks, and gives the impression of being disheveled. I think Craig wins style points here.
I've now watched two debates and several videos featuring Dr. Craig. As I said previously, he's organized, eloquent, confident, and he rattles off his arguments and various relevant (or irrelevant) citations cleanly. Where I have a problem is the fundamental non necessity of the supernatural in explaining the world. I see a creator, supervisor, personal intervener entity as even more unnecessary that the mere supernatural. The immateriality of a deity, and the resources required to implement heaven and hell, mete out reward and punishment for all eternity, and the basic absurdity of such a system based on a few decades of adherence or rejection of supposed rules, is absurd.