Is it useful/appropriate to answer questions for which an answer has already been selected as the right one?
If you have a better answer to contribute than the existing answers, you should definitely post it, regardless of whether or not an answer has been 'accepted'.
In fact, there's never anything wrong with posting a new answer to a question as long as you have something new to add. Adding an answer that repeats information already contained in a previous answer is generally discouraged, regardless of whether or not an answer has been accepted.
Unlike a traditional forum, the Stack Exchange sites do not consider a question 'closed' just because an answer has been accepted. Acceptance only indicates that is the answer that the asker found most useful. Questions are only closed for very specific reasons, outlined in the FAQ. Those are really the only questions to which new answers should not be posted, and the system won't let you post an answer to closed questions anyway. Also quite unlike a traditional forum, the dates on the questions don't matter. I've never quite grasped the concept myself, but somehow, everyone on the Internet just seems to "know" the rule that you don't "bump" old posts. That's not a rule here, or even a guideline to which you should adhere.
What are the chances in your experience that a selected answer might be reversed?
This is a tough one to answer, so I'll just weasel out of it by saying it depends. I've definitely seen it happen before in cases where the new answer is better or more useful than the currently accepted one and when the asker of the question is still active on the site. That said, I've also seen lots of questions where what I personally think is the best answer is not the accepted one.
But remember, acceptance is not everything! Only one answer can be accepted per-question, but the asker as well as other users can upvote as many answers as they choose. It's very possible that there are two or more useful answers provided to a single question, and each of those deserve to be upvoted.
Even if your answer is not ultimately accepted, you should not take that to imply that you haven't contributed something useful to the community.
Is it considered inappropriate to submit a new question by motivating that the currently 'green' answer is misleading?
Yes, it would be inappropriate to start a new question based on the premise that the answer to an existing question is invalid. Your first instinct was a better one—you should post a correct answer to the existing question, instead.
Of course, if you have a follow-up question about an answer to an existing question, that would be a perfectly valid reason to start a new question.