This is in part a response to Robert Cartaino's comment on Suresh's comment response here. I wanted to separate it out from the other discussion, though. I'd like to start by contrasting two questions, one on StackOverflow, and one here.
First, consider How do I move the turtle in LOGO, especially the history of edits and closes. A simple question with a simple answer, and, instead, it was repeatedly edited and closed by users who decided the question was fake, had nothing to do with programming, etc. In this case, the asker was someone who wasn't leaving, so he clarified his position and eventually got an answer.
Now consider the question about disproving the Church-Turing thesis. In this case, I answered the question, it received a lot of upvotes, and was accepted by the asker. However, in the months since that occurred, some of the finest minds in TCS have commented or answered that question, both explaining how wrong I was, and also sharing deep insights about the issue.
A question I'd like people to consider is: Would you rather have a culture of arrogance, in which anyone with enough rep can decide, "Get real, you couldn't possibly be Donald Knuth, I'm closing your question," or would you rather have a culture in which leading researchers feel comfortable adding to a question where a fairly high rep user already posted an accepted answer?
The question behind this question is, "Why is there such a difference in the two sites?" I believe the answer lies in StackOverflow's fallacious belief that crowdsourcing is the best way to arrive at truth. This may be the case for questions at the level of an Ask-the-Audience game show -- or even most in-the-trenches programming questions -- but when literally only a handful of people know the answer, and there are plenty of ways to deceive yourself that you solved the problem (when you didn't), the method breaks down. Crowdsourcing does not produce truth; it only produces an answer that nobody feels like debating any more. This lack of debate might arise because everyone is convinced, or because the few people who know the real answer don't see the point of participating.
Suresh has made the point well that a one-size-fits-all perspective about StackExchange sites does not work. However, I believe this argument does not go far enough. The quality of questions and answers on StackOverflow would significantly increase if that site were broken into smaller pieces. If quality in answers is the priority, it should be harder than it currently is for C# experts to answer functional programming questions, as one example. Rather than the academic caution that we have inherited -- not wanting to brashly say things about a field we know little about -- the StackOverflow model encourages people who get lots and lots of upvotes to answer questions in areas where there is little participation, because they'll get even more upvotes, and the people who know better aren't around, or don't want to start confrontation by calling them out.
Right now, on cstheory, if someone created a profile named "Donald Knuth" or "Avi Wigderson" or whoever, and asked a question, I bet everyone would be careful to treat that user like any other, and to treat the question professionally. The content of the question is what is important, not "making sure we're not being trolled" or whatever. I believe this attitude comes from our common belief in the importance of truth, as something beyond, "Good enough," or, "This is what works." Moving forward, I think the most important thing to bear in mind is that we want to attract members who share that understanding of the primacy of mathematical truth. That's what we share with others interested in theory.
StackExchange, of course, gets revenue as a function of number-of-hits, so I am sure they see the high traffic of StackOverflow as a great thing that should not be messed with by separating out pieces of it. Ok, fine. But if they are interested in more crossover among disciplines, they could, for example, institute a tag system that crosses sites. So, for example, a chemist posting on biostar about the degree sequence of a molecular graph could see questions about degree sequences on cstheory -- and the graph theorist here could see a potential application for the theoretical work! Personally, I would love such a feature. I'd like to ask Joel Spolsky and Robert Cartaino to work on that, instead of asking us to adapt to the StackOverflow site model, which would not serve us well.