When I use link to comments section with name (link looks like www.domain/cat/post.html#comments). Should I use nofollow if just left to this link there is another, without #comments part?
I would have to say yes, put a nofollow on it. But are these 2 links on the same page, with different anchor texts?
www.domain/cat/post.html#comments and www.domain/cat/post.html are considered by Google to BOTH point to the same page... www.domain/cat/post.html. Google ignores everything after the hash ('#') because they are used to point to named anchors on that page NOT to point to a new page. Nofollowing internal links are worthless. I would leave it a followed link. It's the actual comments themselves that point to OTHER sites owned by the people commenting that you want to NOFOLLOW. If you don't and someone drops a link to a "bad neighborhood" site as part of a comment and they get caught for violating Google's webmaster guidelines then YOUR site can be penalized as well for promoting a "bad neighborhood" site.
I will filter comments for "bad words" and if I'll find something spammy, I'll delete these comments and ban their authors via IP's.
Ptutting a nofollow on the name could prevent the link juice to pass to other site which is good for your site.
You should not use nofollow in that as it is going to point your own page. If you are pointing to any external page or a page that you don't want to prefer should be putted in nofollow.