Do you know if a MO analogue exists for college math and mathematics competition problems for undergrads/ high school students? If not, how labor intensive would it be to start such a site? This would provide a venue for young people to share quality mathematics worldwide. (Moderation will perhaps be difficult at first, I imagine, due to a high number of submissions...but this would equilibrate eventually, as talented young mathematics students would eventually uphold the quality!) The hope is that this would provide a venue for generating a global problem-solving community for those who haven't yet become professional mathematicians. Those of us in small colleges could use the site as a source of interesting ideas to engage our students.
There are, of course, obvious disadvantages to such an idea, such as the difficulty of designing quality problems of this type. It just seems that a lower-tier MO would be nice for students. Perhaps call it something like "Student Math Overflow"
This is essentially the purpose of artofproblemsolving.com, if I'm not mistaken. I wasn't really into contest math in high school so didn't use their site much, but one of my friends tells me that it is getting taken over by spammish stuff.
Yeah, AoPS used to be paydirt for that sort of thing, but it's been taken over by the gamers and spammers of late.
May I suggest seeding the new Math SE site with these sorts of questions once it goes to public beta? The mathematical level at the moment is somewhat lower than what you describe, but it's only been two days, and recently there have been some questions that are more undergraduate level. I think it will end up catering to a few largely distinct communities (undergrad math-and-related majors and casual vistors so far--I think adding precocious high schoolers and problem solvers to this would be feasible and worthwhile).
I wondered about AoPS, but it seemed to lack the "back and forth" of MO. My biggest concern with my idea is that it would degenerate into a fast way for undergrads to knock out homework problems. Moderation of this may be hard, because moderators would have to keep a keen eye open for students looking for solutions to their homework. The dream would be that the site I suggest would be a home for open questions requiring only undergrad background, or for an active exchange of Putnam-type challenge problems. The "reputation" system would provide an external incentive that would make the site a "perpetual IMO". You could play whenever you want to...free of charge.
Let me go check out Math SE...I'd never heard of this.