I'm fairly new to SO and particularly to meta as I'm sure is obvious by my rep. As I understand things the accepted answer is the answer the author says answers the question. The user who supplied the accepted answer is rewarded with 15 rep points.
The votes on an answer determine what the community thinks is most useful and the answerer is rewarded with 10 rep points for each vote.
From what I've read so far it seems as if people are assigning to much importance to the accepted answer instead of paying attention to the votes. I can she how the name can be imply that this answer is correct and all others aren't as good or may even be wrong. This is even more likely to be the case for non-SO users who come here from a Google search for their problem. This misunderstanding may be enhanced by the prominent role accepted answers appear to have on the site.
There also seems to be an issue regarding why only one answer can be accepted when the question may be best answered with pieces from several answers.
I have a suggestion that addresses both issues. Please remember that I'm new and be kind...
I think the role of the accepted answer should be diminished. As it is it seems that it really should only be important to the person asking the question and the one who gets posts the accepted answer.
I suggest that each question be given a special fund of 15 points that can be distributed by the question's author across all the answers that helped answer the question. Instead of displaying a big check mark next to the accepted, display a smaller one and a number indicating how many points were awarded.
Also consider not highlight the accepted answer(s). Between that and the big check all eyes go straight to that answer. It might be better to highlight the answer with the most votes as the community is likely a better judge of what will be useful to everyone (not just the asker) then the asker.