It is almost four years that I wrote the following in a thread on the relation of math.SE and MO:
[...] it is from an MO persepective my opinion that a certain type of question that in my opinion used to be more present on MO, and I assume this is precisely the type that now might be asked on MSE, starts to be lacking on MO. What I mean are perhaps too vaguely described "solid graduate level questions" (not the most standard textbook-excercise question from some graduate Analysis or Algebra course but, quoting the FAQs emphasize mine, "the sorts of questions you come across when you're writing or reading articles or graduate level books"; in other words question that are a bit beyond what one can find in any book on the subject but questions that might come up when thinking beyond what one read).
I believe that, ultimately, it is the smaller number of this type of questions that causes the at first glance paradoxical situation that on the one hand some people say that the level of MO significantly increased while at the same time I see some (at the strict/high-level end) users say that MO used to be better.
As Neil Strickland remarked questions arising in the study of graduate level books are on-topic. Arguably, it also should not be forgotten that the site was founded by then graduate students.
That being said the quality of a question is not only determined by its difficulty. Furthermore, in my mind, the level of a question is not only, and not even mainly, determined by its difficulty; for example, the context in which it is placed can be key to evaluate the quality of a question.
Criteria which I find relevant too include:
- clarity of presentation
- interestingness and relevance
- prior effort
for a question to be at research-level I'd ideally expect that the presentation is in a form in which mathematics is usually written by working mathematicians (exception and accommodations can be made for users' having severe language-problems).
for a question to be at research-level I'd ideally expect that it is explained why the question is interesting and relevant to the asker. ("I was reading about subject S and this question Q that I find intriguing just occurred to me." can be a valid explication.)
for a question to be at research-level I'd ideally expect that the asker made some prior effort to answer the question by themselves; e.g., the asker checked the Wikipedia page on the subject, as questions answered on the Wikipedia page on a subject usually should not be asked on MO.
Of course, the answer should not be too obvious either, but in my mind to place too much emphasis on the mere difficulty is not the way to go. There are plenty of worthwhile question that ultimately have a rather simple answer, while there are also plenty of questions that can be very difficult but still are pretty bad questions, as they might be cryptic, unmotivated, besides the point etc.
Now, what does this mean, say, for exercises from a graduate level book or related questions. My advice would be to try to write a questions that does well on the criteria other than "difficulty" I mentioned.
It is my impression that not few users have a serious distaste for question they perceive as "lazy." Thus, something that is (or also just looks like) a sloppily copied textbook exercise or homework problem can be faced with opposition, while the essentially same question embedded into a carefully crafted post giving some context and motivation might have done just fine.
While one should not take this too far, I think it is fine that criteria other than the mere mathematical difficulty play a role in evaluating the suitability of a question; this is also common in other contexts, such as evaluations of manuscripts submitted for publication.
Finally, it is also a goal of MO to provide a place where one can somewhat casually learn about some mathematics in fields other than one's own, as a consequence of which a reasonable effort should be made that posts are accessible to a general mathematical audience (and not just a few experts in the respective subfield).
To sum this up: I think we should be open to well-written and considerate questions at a solid graduate level. By contrast we should continue to put on hold posts that seem like poorly done copy-paste jobs, ideally giving an explanation that a revised version including some context and motivation might be acceptable (if this seems to be the case).
For illustration of the above let me mention the distinct versions of the same question: the former was in my opinion rightfully closed, while I just voted to reopen the latter.