Some really good answers get lost in the shuffle. Perhaps a "answer of the season" would be a convenient way to bring excellent answers a wider audience. Obviously the nomination process would have to be worked out so that not just anything can be nominated to get undue attention. There would no doubt be some kinks to iron out but I would appreciate the the availability of quality answers. The easiest way of implementing this would be to use star rankings (1-5 stars) instead of or in addition to up-votes. That way not just popular questions get upvoted, but they also provide some notion of the quality of the question. Dunces like myself can then easily see what good question look like =) as well as sort stack exchange for quality answers over a given time period.
select the top answers of the week/month/year. ... could connect new visitors with the best of SE and thereby inspire more to engage with the community
I completely agree with this part. We should do something like this, highlighting best content of the week or month on our blog -- the link to which conveniently appears in the sidebar for everyone visiting the site. Ahem, except that there is no Math.SE blog yet.
I completely disagree with the idea that crowd-sourced statistics, be they arrows or stars or stripes, can determine the best quality content on a mathematical website.
Furthermore, I do not believe for a moment that SE would introduce such a feature. All SE sites run on the same engine, which produces unified HTML markup of the pages: here and at Home Improvement and at Christianity. A feature that changes the way in which users interact with the site has to be implemented everywhere. It has to be something that can win the support of meta.SO. This feature isn't it.