What are the guidelines? Will the moderators take action OR does someone have to flag it as "Known Unsolved Problem" or "Known Open Problem".

For instance question here was about a Diophantine Equation that is listed as Unsolved.

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That is one reason I go about asking people posting number-theory related questions for the source of the problem... –  Aryabhata Mar 25 '12 at 19:57
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There also is the open-problem tag. –  Martin Sleziak Mar 26 '12 at 14:16
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1 Answer

I think that an answer explaining that this is an open problem and perhaps listing a few sources for that (and maybe conjectures on the possible answers) should be a good step, no need to alert the moderators.

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I wonder if we're talking about a situation where OP knows it's a known unsolved problem and withholds that information. I could see where the moderators might want to know about such behavior. –  Gerry Myerson Mar 26 '12 at 0:58
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@Gerry: yes, and it would be ironic if we can get a new closure reason "closed as 'known open problem'". –  Willie Wong Mar 26 '12 at 8:15
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I can imagine the topologists saying, "Sure, a question can be simultaneously open and closed, what's the problem?" –  Rahul Mar 26 '12 at 10:23
    
@RahulNarain: Let $\alpha<\omega_1$ can we find a question which is $\Sigma^0_\alpha$ but not $\Sigma^0_\beta$ for all $\beta<\alpha$? –  Asaf Karagila Mar 26 '12 at 10:32
    
@RahulNarain Your last comment was hilarious, even if it is incorrect. :-) –  Hardy Apr 2 '12 at 8:20
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