Who would check it ?
I would love to have some sort of utility like this, but it's practical use would not work.
Who judges a correct answer ?
It is perfectly feasible that the first answer could be right but that the person asking does not understand it and unchecks the mark.
It is also possible that someone unchecks (or checks) an answer which uses technical language or which uses simpler language.
We would certainly have certain people who inhabit here checking their answers to people both before the asker had seen it and when their answer was clearly wrong to everyone else on the planet.
There could also be a call for statistics about who answers the most right, who deserves this / that / the other.
Here I go again, stomping all over ideas proposed .... I hope you don't see it that way. This has been talked about before and it is definitely something that would be good, but for the reasons above and more it becomes impractical. Which is a shame.
For now, I would suggest that good answers could be tagged in some way and maybe moved to the Codex FAQ ?
In the end though, there is only one person who can say whether a question was answered - the person who asked it. And that is why it is both great for the answerer and even better for the community when someone posts back and says "Cheers, that worked!!"