What should our comment culture be?
Stick with the SE model as much as possible. Use comments to request clarifications, suggest improvements (and thus, also explain your voting patterns a little) and be weary of sidetracking into different discussions.
That said, on a new beta you're probably bound to write some longer comments, sometimes posting 2 instead of one due to character limits. This isn't necessarily bad, it's a new site with new users and carefully explaining why you e.g. vote a certain way on questions or ask for a specific improvement can work wonders in helping people understand why they're getting the feedback they're getting.
After a few days, you may notice that you've written comments saying the same thing, pointing out the same problems on posts, several times. Or more than two users are getting involved in exchanging their ideas on a post. At that point, you have valuable, practical examples to start a focused meta discussion about which posts are suitable questions or answers for the site or not.
How might we moderate comments? What should we flag, and when?
I'm not fond of moving things to chat, as that hides a lot. If comments are pointing out relevant improvements or clarifications, there's not much sense in hiding it in a post specific chat room. Sometimes, when more controversial/heated discussion is moved to chat, that chatroom also becomes the room you put a smelly cheese in... If you open it after a week, it's a bet between the cheese having aged fine or the whole room stinking. Often, it's the latter. IMO, if it doesn't belong on the post, it rarely belongs in chat.
As a first principle, I would suggest using common sense and trying to stick to the purpose of comments (clarification/improvement of a post). Besides that:
- If you used comments clarify parts of the post, edit those in and delete your own comments/flag the related comments for deletion. If as a third-party you see comments that have been edited into posts, or are otherwise obsolete, don't be shy to flag. Enough flags from the community saves moderators work.
- Flag and delete those comments that aren't related to discussing moderation or improvement of a post at all. The example that sparked this question was a comment thread on a question explaining a reason for close-voting in detail, that eventually side-tracked in discussing the comments on that question. At that point, the discussion is no longer directly related to the post and has to stop, move to chat or in this case, to meta.
- Strike a balance between comments that explain a problem within a post and are a back-and-forth between the person that posted the question/answer and a commenter, and explain e.g. close-votes, and 20+ comment threads between several users that should've been a meta discussion. Don't be shy to mention that something should be on meta, either linking to an existing discussion or creating a new one.
- Don't drag out comment threads endlessly. This carries the greatest risk of sidetracking. If you notice you're drifting away from the main point, it's probably time to call a halt to the thread, point to an existing meta discussion or make a new one, and flag the comments from the point the sidetracking started.