Sometimes I receive answers that would solve my problem, and seem plausible, but I don't know whether they're correct, or if they're the full story.
Should I accept such answers immediately? Or should I wait a day or so until they've received some upvotes (hopefully not just everyone else saying I don't know if this is correct or not, but it makes sense to me!) and no comments or disagreeing answers?
First of all, you are recommended to eventually accept one answer unless there is a good reason not to do so.
However, you do not have to accept an answer as soon as possible. I think that it is generally a good idea to wait for one day or two before accepting any answer. This way, other people can post a counter-statement if they find anything wrong with the answer.
It is not a good idea to wait indefinitely until your are convinced of the correctness of an answer. If it takes a long time for you to be convinced, there may be something wrong with either your question or the posted answer. If the answer lacks a verifiable source, it makes a perfect sense to ask for one by posting a comment on the answer.
Accepting is up to you. You have no duty to accept answers that satisfy other people. If you never get a satisfying answer, then
If you think you'll never have a satisfying answer, well, then, maybe it's ok to never accept any answer, but then, maybe the question should be tagged as "open-problem"…
