I think more of an issue are completely definitive answers that are left "unchecked". There are a non-trivial number of questions which have thorough and incontrovertible answers, but, for some reason or other (the OP never came back to look at the responses) are not marked "answered".

Why is this more of an issue? The check mark is a nice way to close the social loop and/or indicate that the question has been answered to the complete satisfaction of the asker, but an answer doesn't have to be accepted for everybody else to see it. Since the answers are sorted by votes, definitive/clever/clear answers will be at the top anyway. You should worry about people not voting on answers much more than you should worry about people not accepting them.

"+1: Great answer, even if it doesn't fully answer the question." "+1: I'm not going to accept this, as it's not complete answer, but everyone should vote this up because it's very helpful." "I've accepted this answer as it seems it's the best we're going to do for now."

etc.

I think it's perfectly okay to accept an incomplete answer. Your main consideration should be: "Will the page be more or less useful to future readers if I pin this answer to the top of the list, and indicate that it's the most important thing to read?"

Don't think of it as a referee would: you're not stamping your approval of the completeness or correctness of the answer. Instead, you're trying to make the page helpful for people trying to learn from it. (Of course, often, and ideally, these goals coincide.)

(a) if you are the question poser, you are free to use whatever metric in assigning credit. On one end of the spectrum you can even "accept" Snuffleapagus's anwer while leaving a comment that it doesn't solve the original question. On the other end you can just do nothing. In the middle you can encourage other people to vote it up. But remember that the design philosophy of the software underlying MO is that "one user one vote", and crowd sources the decision of good answers, while giving the question poser an effective veto power to accept an answer he finds more suitable. Changing the system would entail changing the MO philosophy.

(b) Speaking of software, remember that the software that MO runs is effectively out of our collective control (belongs to Fog Creek), and since the release of SE2.0, there probably won't be "feature updates" even if we ask. So unfortunately any discussion will be eventually moot.

Now, I'm in favour of the idea of just coming to Meta and say: hey guys, there's a very nice, but incomplete answer to one of my questions, would you mind voting it up so it would be bumped to the top of the list, since no other better answers are available? I'm sure many will be more than happy to comply.