I have often imagined debating William Lane Craig myself, and thought out the ways I would respond to his arguments. I have often, while listening to Craig's debates, wondered why his opponent didn't call him on some claim that was simply untrue. Were they just being polite, or did they not realize the falsity of the claim?
I think I may be cured of these fantasies. Sean Carroll did brilliantly in the debate - far better than I could ever have done. He didn't hesitate to say outright, "That's just false!" And his deep expertise in cosmology was the perfect counterpoint to Craig's quote-mining of partially-understood physics papers.
I have only a couple of comments on style and content. I thought Sean did a good job of pointing out where Craig failed to respond to the argument. (This is an area where Craig usually excels.) But instead of merely pointing it out, he ought to have taken the opportunity to summarize his argument again, for those who might not have understood it completely the first time.
Craig, as usual, excelled in his logical organization and presentation of his argument. His concluding summary nicely recalled his original point: not that he was out to prove God's existence, but that modern cosmology lends support to one of his premises.
Here Carroll really missed an opportunity. He ought to have said, briefly and succinctly, that modern cosmology lends no support at all the premise that the universe had a beginning. What we can say for sure is that the universe was a very different place 13.7 billion years ago. But any statement about what happened before that is very speculative and unfounded in established science. There are models in which time has a beginning, and there are models in which it doesn't: none of these models are established science, and so nothing can be deduced from them about a beginning.
One final missed opportunity: when Craig asked, quite reasonably, "If universes can just pop into existence, why not bicycles? What's the difference?" (from memory, not an exact quote) Sean could have responded that there is an obvious and crucial difference: bicycles are things that exist within time, while universes are not. On the contrary, time exists within a universe. For all Craig's bluster about simultaneous causation in the Q&A session, causality has to do with what brings about a change. And for there to be change, there must be time. Since a universe is not something that happens in time, the causality issue doesn't apply.
I think Sean probably had something like this in mind in his argument about the a cosmological model as a self-contained description needing no outside cause, but it would have been nice to respond to Craig's question with a specific difference that clearly matters.