I'm not sure I see any problem with it in general, though I have caught myself being somewhat annoyed when I've seen a good or correct answer given on one site then the question gets asked again elsewhere.......fits in with the "looking for the answer you want....." idea. Other times, when multiple answers can be "correct", I think there's value in different perspectives. I'm more peeved by the "why does my car run rough......?" type of question and people (however well intentioned they may be) on multiple sites do the guessing game rather than try to zero the questioner down with more diagnostic info first.

Then to use Jay's example, you end up giving the same response on two sites because other folks at either have "spin off" questions that prompt the repetitive response.