With a man on 3rd the umpire believes that there are 2 outs in the inning. The batter misses 3rd strike and the catcher does not catch the ball. The batter runs to first and is call out. The runner on 3rd base then comes home and is safe. The team on the field comes off the field and then everyone realizes that there are now only two outs. What should the umpire do?
First off, I am going to cover the situation about the confusion with the number of outs. Even though there sould be no reason why the umpire should lose track of the number of outs since most ball and strike indicators have an out area on it, every once and a while something weird happens that makes the umpire forget the number of outs. If this happens the umpire who forgot how many outs there were should check with the other umpire using the signals that they should have discussed before the game. If neither of them know the number of outs then one of them should check with the official scorer to find out how many outs there are. Also, the coaches and players should know the situation and remember how many outs have been made in an inning and if they have any doubt they should check with one of the umpires.
In this situation the offensive team should not be penalised for remembering the correct number of outs while their opponent did not and the run should count. Coaches and players must be focused on the game situation at all times and should bring any possible confussions to the umpire so he can sort the problem out (as mentioned above). Since in this situation it is obvious that someone remembered the correct number of outs there was no confussion on a previous play about if an umpire called someone safe or out.