"I've heard that betting markets generally have a good track record of aggregating the views of people and pointing to reasonably correct results, as long as there's enough participation and people have something real at stake"
In my opinion, there is no reason to believe that prediction markets will be useful to aggregate information which is not there. For most mathematical and scientific questions people have no real information that aggregating together will say something useful.
It is not clear also how good are financial markets in predicting their own future behavior. (But it is a complicated question how to formally as it.)
It would be useful to look skeptically also into these claims about the good track record of prediction markets that the asker heard about.
Probably the question is more suitable to a "meta discussion".
Further discussion can be found in this post over Shtetl optimized following this one.