I've done some fiddling that, hopefully, will finally end the problem you've been having with incorrect "new comment" numbers.
The gory details:
To try to increase performance on the site, I enabled "caching" on items on the home page - instead of making several database requests to build the page, the system grabbed a single cached view of posts. The problem was the cache was not updated when somebody commented on a post, leading, I think, to the incorrect numbers. To get around that, I've enabled a different caching mechanism, which updates the home page whenever somebody comments.
Please let me know if you still run into issues, though!