After an answer is accepted, sometimes a much better answer comes along. While an original poster gets notified of new answers, there is currently no notification if a different answer garners far more votes than the accepted answer. It would be nice to nudge the OP to reconsider whether the originally accepted answer is still the best one.
This kind of reminder would help prevent the case of a long, accepted answer causing a far more popular answer to not appear with the initial viewport. It's easy when you see a comforting accepted answer mark and reasonable vote count to forget you might be better off scrolling first and reading later.
Another benefit is that less experienced users would learn that they can change the accepted answer (I think many don't know that).
My suggestion for a notification threshold would be double the accepted answer's vote count with a 10 vote minimum. Follow-up reminders would be good at 4, 8, 16, etc. times the accepted answer's vote count.