I have at least two questions which are about graduate level mathematics on Math.SE, but about which I have serious doubts regarding whether or not they are "research level". In other words, I don't think they are open problems, but then again I don't know enough to confirm that suspicion either. I also suspect the reason why they are unanswered on Math.SE is that they are just uninteresting, but at least one of the questions has enough upvotes that that seems somewhat unlikely.
Also for the record, I am going to wait at least one week (both questions are still only a couple of days old) before actually considering re/cross-posting them anywhere.
I have a lot of reluctance to post on Mathoverflow, even if my questions are appropriate, because the only research I have done was in applied mathematics which used a lot of numerical simulations to form conjectures, and though I have at least the prerequisites to study graduate level algebra/topology, the only graduate level mathematics I have seriously studied is in analysis and probability theory (although I do want to rectify that somewhat now that I am done with undergrad); also I am pursuing a PhD in statistics, not pure mathematics, and as one commenter on Math.SE put it "statistics is a well-known easier subsubject of mathematics, so any question you could possibly have about statistics could be answered on Math.SE".
I know there are people who do statistical research without mathematical rigor, but personally I am of the opinion that if one is not utilizing the full amount of mathematical knowledge which applicable to statistics (which even exceeds the reified realms of analysis and probability theory) is not doing such research correctly. Admittedly this might be a minority opinion.
Anyway, if anyone thinks the two questions I linked to above are stupid, please let me know, so I don't waste anyone's time in a week or so trying to cross-post them here if they don't receive any answers on Math.SE.