I noticed today that a used had asked the same question both on math.SE and on cs.SE (see https://math.stackexchange.com/questions/181291/which-languages-are-decidable#comment417845_181291 and https://cs.stackexchange.com/questions/3119/is-it-decidable-whether-a-tm-reaches-some-position-on-the-tape). The user indicates on another comment that they do this routinely:
Usually when I post there, I don't get answer for couple of hours,so I post here, get answered very nice and fast, and delete my question from csStackexchange.. [comment below Can weight-restricted versions of monotone 2-SAT be decided in polynomial time? ]
The double-posting seems problematic to me, particularly since the questions are being upvoted on both sites. That indicates to me that people are thinking about them on both sites - and the users are not all the same between the two sites. So someone is likely to spend time on a problem only to find that it has disappeared. I think it would be preferable for the user to, at the very least, indicate on the question that it has been posted elsewhere. But ideally the question would just be on one site, so that all the discussion would happen at the same place. To some extent, when a question is on topic for multiple sites, I think it's better to commit to one site for a while before trying another, even if this means the answer is slightly slower.
I tried voting to close this particular question on math.SE as a duplicate, but the system only allows that for same-site duplicates. I tried asking for it to be migrated to cs.SE, but the system doesn't include that as a suggestion.