Since I was one of the "delete" votes for "Riemann Hypothesis", I'll present my standpoint here.
In that particular instance you do not need to know pretty much anything beyond elementary algebra and a little bit of undergraduate complex analysis to evaluate that "proof of Riemann Hypothesis" by yourself or to ask your friend or colleague next door to do it if you are too lazy. Dragging such obvious nonsense to MO is more or less equivalent to spamming, IMHO.
Reuns responded in a very precise manner to it, leaving no uncertainty about the issue whatsoever. I was way more harsh (to the extent that my comment was, apparently, deleted by moderators). But no matter which way you look at it and what you say (or agree not to say) about it, a piece of junk remains a piece of junk.
This much said, I see nothing wrong about discussing the correctness of some proofs that can be classified as "correct" or "flawed" in principle and for which figuring out the answer requires some expertise in the field. Ideally, in such cases the OP should pinpoint a particular place that bothers him in the argument, but this assumes that he has sufficient qualifications for that, and that is, obviously, not always true. So, I would decide such issues on a case-to-case basis without trying to make any general rule at all. If there is somebody who is qualified to answer and is willing to spend his time on the investigation, I see no reason (and no moral right) for anyone else to interfere with such attempt. If nobody answers, than it is fine too: no one is obliged to think of any particular question no matter how well it is posed.
In general, my main premise is that MO is about mathematics and not about the formal rules for the posters and respondents. If somebody asks a meaningful and non-trivial question about mathematics and somebody else answers it in a meaningful way, why should anybody else care what exactly that exchange was about?
This question does not appear to be about research level mathematics within the scope defined in the help center.does not quite apply I believe. And, although I agree with the comment
"Is this preprint correct" questions are off topic., I don't know how to answer the question "How would I know they are off topic?". $\endgroup$
quid, right? $\endgroup$