Mother's will lists her 4 children as inheritors. One son has died. Does the will need to be updated?

Yes, it should be updated. In my research on estates I have come across this issue (sorry, don't have the links at hand) and it can get messy. To avoid the mess, update the will.

I don't know from a legal standpoint. But I would suggest she have it updated if she wants the distribution different. As it is now, I believe the inheritance that would have gone to the deceased son would go to whoever his heir was - which could be his wife. If your mom would rather her deceased son's inheritance to go to his children instead of his wife, she will need a new will. Or if she would now rather the inheritance go to the remaining three children, I believe she will need a new will also. Good luck!!