I think it would be nice to be able to write comments at every problem statement. These are some reasons:
Having all the comments about a problem in one place. Currently the only way to ask a question is to find the editorial page (or the announcement) or create a new blog post. Sometimes I read a long discussion about the problem X without understanding anything just to realize that they are talking about the problem X of the other division (yes, I'm that stupid).
Many editorials are useless in my opinion. They usually have a couple of sentences for each problem that do not help if you don't know how to solve the problem. I've seen things like: "this can be solve using a variation of the XXX tree" but you don't actually know which variation is or why this variation solves the problem. In contrast, other editorials are really good. The Rockethon editorial for example written by Gojira is awesome.
Some people have their own blogs where they write in-depth about the problems they solve and some of these posts are good enough to have a link at the problem page but currently there are only links to the announcement and the tutorial. This could be done adding a comment.
I think this will be a more ordered source of knowledge for the people who is learning.
Probably there are more reasons and maybe even some reasons to not implement these comments.
i think we can also include a link to Round Statistics usually posted by DmitriyH.
this can possibly be done on the contest page, if not on problem page.
I prefer the remedy against these stupid spam posts like "Precise copies of Swiss enlarging boots" is found first.
Otherwise these comments for problems would also be collectors for such spam.
And BTW do you want to include "comments for problems" into the general "recent action" list?