#1 - he missed the point of the debate and ended up not defending the position he was supposed to take. The debate was whether or not contemporary cosmology gives good reasons for belief in God existence. WLC presented big bang cosmology as a reason for that belief. It's a darn good reason because the model's success is attested to by virtually every scientist except for a handful of them, cosmologists, who don't like it's implications. It calls for a causal explanation for the beginning of the universe. Carroll, on the other hand, said there are plenty of successful models that explain the existence of the universe apart from a "beginning" so to speak. There are at least 3 problems with this response.
First, it either kicks the can down the road or says that something came from nothing. An infinite regress is logically impossible and there is nothing in nature that suggests it could be the case; e.g., the second law of thermodynamics. SLOT is scientific evidence against infinite regress. So, that option is out and WLC addressed that pointedly. On the latter, he took issue with WLC saying "popping into existence." Well, if you don't posit an infinite regress and you don't believe in God, then you necessarily believe that the universe came from nothing, at some point. This too is problematic because ex nihilo, nihil fit. WLC also addressed this pointedly.
Second, the models Carroll cites are theoretical proposals based on mathematical probabilities, not evidence. They are nothing more than fanciful uses of scientific imagination. Moreover, as WLC pointed out, cosmologists are far separated from any kind of consensus on any of the models but, Carroll continued to talk as if science were empirical and objective, which was specious. Big bang cosmology is far from a theoretical, speculative model and has multiple aspects of scientific confirmation.
Third, those models do absolutely nothing to obviate belief in God, which was supposed to be his position. All they do is posit that the universe we live in could potentially have come from another incarnation before it. There is still a wide, wide window for God to operate within in that line of thinking. In fact, it could be that in time, any one of those models will yield similar reasons to believe in God's existence as the big bang model has. What really kills this idea is that it could be that God is necessary for the conditions that caused the universe to come from some prior incarnation. In other words, God might be a necessary causal agent for any of the multiverse theories to either originate or be maintained.
#2 - Carroll kept obfuscating on the main question. He said that asking for a cause of the beginning of the universe is the wrong kind of question. Well, why was he even in the debate then? The whole point was to investigate whether or not known facts yield a positive or negative response to the question, not that the question is a category mistake. If the observed laws of physics are not applicable outside of our paradigm, then why are scientists scurrying around looking for prior causes? Isn't that a category mistake, particularly when the laws of physics are not applicable? Why look for prior causes via alternative cosmological models other than to find ultimate causality? This was not a debate on why cosmological models are successful from a purely methodological naturalism perspective. This was a debate on whether or not they yield insight into the metaphysical, the transcendent, the supernatural. In this regard, he and all other philosophical naturalists are on the losing side. No one will ever be able to prove there is not a God, even a deistic one, much less one that actually intervenes in this world. It would require knowing everything possible, including in other possible worlds even though they operate differently. This is clearly impossible, even from a hypothetical standpoint. The theist, on the other hand, does have good reason to believe in God.
BTW, did you notice that Carroll made multiple appeals to the "laws of physics" that the universe operates according to but then, on multiple occasions said that the universe will operate in different ways in different places. This is duplicitous. So, which is it? Are there immutable, ubiquitous laws or not? This is called special pleading. He gets to say that science has the advantage of "facts" on its side because it operates according to laws that invariably predict outcomes (methodological naturalism). They have been honed for at least 200 years. He also gets to have instances where "anything goes" because of how diverse the universe is (supernatural speculation). This means that scientist are free to invent theories no matter how fanciful and they are somehow more plausible than the big bang model which has been vigorously confirmed by science. Whenever WLC would make a point about natural phenomena, Carroll would bounce out to the strange and wonderful multiverse and act like WLC was ignorant. Then, when WLC would comment on something about the multiverse like the tenseless or tensed nature of time outside of this universe, Carroll would jump back into this universe and talk about the immutable laws of physics and his rock solid empirical worldview. Convenient.
In the end, Carroll is obviously authoritative about cosmology but, not about metaphysics. In contrast, WLC is authoritative in that regard. He understands clearly the demarcation problem, even though he didn't address it. WLC certainly worked harder than necessary to undermine Carroll's points.
Last, what was that irrelevant diatribe on naturalism vs theism? Carroll was even more wrong about that which isn't surprising because he's a scientist, not a philosopher.