So nothing. Admission of error is all the NFL will or can do in such a situation. It is bad enough during the regular season, but try it in the playoffs. Ouch.
Referees should be younger, more fit, better eyesight: recent retirees from the league might be best...not guys in their 50s who never played and sadly cannot see very well.
NFL referees typically start refereeing at the HS level, move on the college level, then to the NFL. The selection process is stringent and for those referees who make it to the NFL level their performance is monitored weekly during the football season.