Downvote and (optionally) comment the old answer, upvote the new answer.

This actually has a twofold effect. It notifies the OP of the old answer that there may be an issue that needs to be addressed, and it also serves to begin the process of floating the new answer to the top and dropping the old answer to the bottom.

If the old answer is accepted, there may be issues there, but a note to the OP of the question that the ruling has changed is not out of line. In rare cases the answerer of the accepted answer will realize it's incorrect and that there is now an established correct answer and want to delete their answer. In this case the OP should flag it and ask the moderators to delete their answer since they cannot do it themselves. Moderators are typically quite responsive to these flags (though in rare cases they may see value in retaining the original answer if it's providing other value outside of the incorrect answer).

Downvote and (optionally) comment the old answer, upvote the new answer.

This actually has a twofold effect. It notifies the OP of the old answer that there may be an issue that needs to be addressed, and it also serves to begin the process of floating the new answer to the top and dropping the old answer to the bottom.

If this is still insufficient, you could (and I've done this myself), offer a bounty to award the new answer and thus draw attention to the question.

If the old answer is accepted, there may be issues there, but a note to the OP of the question that the ruling has changed is not out of line. In rare cases the answerer of the accepted answer will realize it's incorrect and that there is now an established correct answer and want to delete their answer. In this case the OP should flag it and ask the moderators to delete their answer since they cannot do it themselves. Moderators are typically quite responsive to these flags (though in rare cases they may see value in retaining the original answer if it's providing other value outside of the incorrect answer).