I have solved a couple of questions myself in the past, and I think some of them are interesting to the public and will most likely appear in the future. One example for this is the question how to enable antialiasing in the Linux frontend, for which there is no native support right now. My question would now be whether posting these as a new question would be appropriate, and then immediately answer it.
If your questions are genuinely interesting or intriguing problems, then posting self-answered questions is generally considered okay.
My only caution this early in a beta is with regard to asking questions simply to "seed" the site. Stack Exchange sites don't generally need to be seeded for the purpose of adding bulk. Take a look at this blog post:
But if you're question is interesting, certainly… feel free to post.
Most of these answers say, "If it is interesting, ask it." But what do we mean by "interesting"? Or more appropriately, interesting to whom?
If we want only Mathematica experts to visit the site then we should probably ask questions only an expert would ask. I'm of the thinking that we probably want some frequently asked beginning and intermediate sorts of questions to draw new users to the site.
I say this for two reasons. 1: we don't want to scare people from asking simple questions. 2: We want to draw people in who are doing a web search.
When I started with Mathematica most of my problems dealt with simple list manipulation and importing data. I also found simple shorthand used in examples (e.g. #, /@, ,__, /., /;) maddeningly confusing.
I wouldn't really be interested in a question about these things now, but I bet many new users would be.