When the idea of chavrutas came up in an earlier discussion with raw power, I noted that the system doesn't always work out the way it is intended, especially when weird social issues come into play.

Having a lot of experience with this system, it does have pros and cons. One serious con as far as LW should be concerned is two-person meta-affective death spirals. What I mean by this is not affective death spirals so much (although that can be a problem) but reinforcing various types of arguments. To use a Less Wrongish example, one could have two chavrutas who really like anthropic arguments. They might focus on anthropic issues to the exclusion of other types of relevant evidence. Continued for long enough, this sort of thing could result in people giving a lot more weight to some approaches which are completely disproportionate to the approaches' actual usefulness.