I have submitted one my client's sites twice in the last 4 months with no results. I also used the DMOZ "feedback" form to ask about the situation, with no reply.
The DMOZ FAQ says:
"We don't accept all sites, so please don't take it personally should your site not be accepted. Our goal is to make the directory as useful as possible for our users, not to have the directory include all (or even most) of the sites that could possibly be listed or serve as a promotional tool for the entities listed."
We are trying to get listed in the HTML editor category:
If you are willing to chip in and edit the category that might be a possible beginner category. Haven't looked at it, but it doesn't sound like something that would be hypercompetitive and if its around 50 sites or less it might be a candidate for a new editor.