At the moment, the most you can do with comments is open them up in your browser.

Could you be more specific about the feature you're describing? Comments are an area I'd like to look at expanding on. I guess you mean tracking whether or not there are new comments on a story?

If you're involved in a comment thread, the discussion stays alive better if you respond promptly. But how do you know if people when people have responded to your comments? You can refresh the page but if you have several threads on the go at the same time, this might not be practical.

Ideally:

1) highlight comments that are new since the last time I viewed the comments,

2) alert me when a new comment has been added a specific thread

Interesting ideas. They're the kind of thing I'd like to look at in the future. In the mean-time, I suppose you're aware of the "Threads" page for each user? http://news.ycombinator.com/threads?id=YOUR_USERNAME_HERE

I use that for keeping track of who replied to my comments and stuff like that.

Yeah, that page is certainly helpful.