I had this same problem, but was able to solve it... I describe how here:
Basically, to solve the comment_count issue, I ran the following SQL query in phpMyAdmin:
comment_count = (SELECT COUNT(
My database has 129 categories, 14,461 posts and 107,302 comments, and the query ran almost instantaneously, so speed should not be an issue.
As for categories, that can be solved without delving into phpMyAdmin. In the WordPress interface, simply create a new post and check off every single category. Save the post. Voila, you’re done. All the categories will update their category_count field. Admittedly, it was a little annoying to manually check off 129 categories, but it was doable, and it solved the problem in one fell swoop.