When I click the "Unanswered" tab, most of the questions that show up are in fact unanswerable - when I click on them, I find they've been merged with other questions and as such are effectively closed. Some have been this way for months. Is this a bug?
This was indeed a bug of sorts. Merging doesn't actually require the question to be "closed", it instead puts it in a different state called "locked" which blocks pretty much every form of activity such as editing or commenting or even voting. The bug was that the "Unanswered" tab filters out closed questions, but did not do the same for locked questions.
As of January 8th, a fix was put in that now prevents locked questions from showing up in the Unanswered list, which means that merged questions should no longer appear.