The "fastest gun in the west" bug has been fixed for awhile; answers at equivalent ratings are ordered randomly. In my experience, that's eliminated the problem 90% of the time and ameliorated it the rest.
A mediocre answer that was posted one minute after the question was submitted often has more votes than a well thought answer posted several hours later.
A better solution might be to randomly order answers, regardless of votes, for the first couple of hours (maybe even day). This will further help remove any ordering bias.
I also feel that authors of answers should be hidden for the first couple of hours (or day). Just because John Resig answered a question, doesn't necessarily mean it's the best response.
StackOverflow should seriously consider using this algorithm, at least for a day since the question was asked, as one previous commenter said.
Optionally, question submitters could pay for "Urgent" status, where the submitted answers are posted as they come in. No ratings or votes would be accepted for the same cooling-off period, however.
The worst case scenario is a question which is perfectly written such that it garners attention from experienced folks who know what they're talking about for only a tiny amount of time, and ever after only garners attention (via google searches, for example) from clueless noobs who can't judge the quality of the answers (and don't have the rep. on the site to vote answers up or down anyway). However, this is a pretty contrived scenario which doesn't play out often in real life. Important questions will garner attention by people with a range of experience and qualifications, which will have the side effect of improving the quality of answers over time through future voting etc.