The incentive for quick sloppy answers comes from the bias of voters towards what's already upvoted, which could be fixed just by showing them the answers in random order without the scores. Maybe change the display mode after the page settles down some, by some measure like time passed, pageviews, or answer accepted.

I agree there's a problem, and used to participate anyway because more fun or interesting questions were getting asked early on; I never seem to see new ones when I peek in nowadays.

Added (heh): people also vote for sloppy answers just because they sound good. I don't know what to do about this -- perhaps you could try to estimate a voter's average vote quality, and weight them.