My question is quite specific: This 2010 question received a seemingly correct answer, but recently it was noticed that the answer is wrong in the sense that it just links to the paper that doesn't really contain a proof. To the new question an excellent answer was given, which shows that quite likely there's an error in the paper. What should be done about this and by who?
If the questions are completely duplicate, i.e. an answer to one would be an answer to the other one then one should be close as a duplicate of the other one. The general practice to close the newer one as a duplicate of the older one.
In this case, it seems that the old one has an accepted wrong answer. Note that moderators can merge questions which would redirect the new question to the old one and move all the answers to the new question to the old question.
Ideally the author of the old question should accept the new correct answer but that is up to the author, we cannot enforce that.
I would suggest flagging the new question for moderator attention and then explaining the situation and they can decide if it is really an exact duplicate and if so merge the questions.