I think that's a very bad idea. Problems are not just regex or non-regex. Sometimes you can't decide if a question is a regex question or not. Lots of people ask for regexps to parse XML|HTML|CSV. (Update: to make this clear, this would be sort of like making a section for homework questions.)
This would be worse if we had a section like that. But that's nor the most important problem.
We could just as well have sections for CGI questions (including templating, generic HTML|CSS|Javascript questions doing nothing to perl, etc), LWP|WWW::Mechanize questions, data structure questions (including how do I dereference this, or sort this by this key), XML questions, bioinformatics quesitions, module installing questions.
Don't you realize how this is orthogonal to the current division of sections? There are regex meditations, regex obfus, cool uses of regex, regexp snippets, regex poetry, reviews of regex modules and regex books. If you continue this, we would get a large matrix of sections.