The debate between Richard Carrier and Douglas Jacoby is one of the best debates on Christianity I've listened to in a while. You can listen to it here (Beware that it's nearly three hours long).
One of the arguments that Carrier made concerned Mark 7 in which Jesus and his disciples are depicted not washing their hands and apparently renouncing the practice of handwashing because, according to Jesus himself: "there is nothing outside the man which can defile him if it goes into him; but the things which proceed out of the man are what defile the man." Carrier reasons that if Jesus had been God he would never have said such a thing because handwashing prevents disease, as we all know. Of course, as I read the chapter in context it seems to me that the point of all this business may not be about actual, literal handwashing so much as it is about Jesus' teaching that what you do is more important than what you eat. On the other hand, since Christians are supposed to live as Christ did, it's extremely easy to see how someone might take this verse and imitate Jesus by not washing their hands, and thereby contracting a disease. It is also easy to interpret the verse as meaning that no harm (or "defilement") whether spiritual or physical, will result from not washing your hands. In fact, I wouldn't be surprised if that is what the verse really meant. You could interpret it another way, but then we're faced with the problem of why an omnipotent God wouldn't be a little clearer in his message and speak in such a way as to not easily allow people to come away with the wrong message. So Carrier has a point, but it isn't the strongest point ever made against the Christian faith.
Another point that came up in the debate which was misunderstood even by Carrier's opponent, Douglas Jacoby, was Carrier's point about schizotypy amongst early Christians. Carrier noted that it wouldn't be all that surprising if some of the disciples hallucinated the resurrected Jesus after his death, because, among other things, new religious movements often have lots of schizotypal individuals within them, and schizotypes are very prone to hallucination. Here is a link to a scientific paper that confirms what Carrier said on this point. Of course, Carrier does not believe all or even most Christians in the 21st century suffer from this disorder. But at least a significant number of Christians in the 1st Century probably did, as Christianity at the point had the status of a fringe cult, and we should expect it had all the features that we usually observe in fringe cults.
It was also mentioned that lots of religious sects have group visions. In a forthcoming book I am writing, I will detail a number of these. Based on a quick search I did, I found two books that detail such occurences, and I know of an excellent book that details several more: Looking for a Miracle: Weeping Icons, Relics, Stigmata, Visions & Healing Cures
Carrier also made some statements about the similarities Christianity has with other pagan religions of the time. I haven't read about all of these myself, though I would not doubt that he is correct as I'm not well read enough on those pagan religions to know. However, what I can say for sure is that there are definitely some strong similarities that certainly suggest influence. See Dr. Richard C. Miller's article "Mark's Empty Tomb and Other Translation fables in Antiquity" published in Journal of Biblical Literature which you can read for yourself here. For anyone else, Carrier also has a book detailing a number of pagan parallels with references and a good discussion of them:
Not the Impossible Faith