An umpire lost track of the count and gave the batter an extra strike. The umpire realized the error and gave the next batter 1 strike to start the next at bat. Can he do that?
First off, there should be no reason why the umpire should lose track of the count. However, if the umpire does lose track there are a few ways to find out what it is. The best way of going about this would be to ask his partner. This kind of situation should have been talked about in the umpire pregame meeting and there should be a discreet way for one umpire to signal to the other that they lost track of the count. One signal that I like to use is to have the umpire who does not know the count tap his empty palm with his indicator. Then, once the other umpire sees this, the umpire who does know the count should either display the count accross his chest or at his waist area.
Another way to prevent this is to have the base umpire display the count at his waist after every pitch. This not only helps the plate umpire keep track of the count but also keeps the base umpire in the game.
A third way to deal with this scenerio is to ask the official score keeper what the count is. This is not the best way to handle this situation but getting the call right is the most important thing.
To answer your question, no, the umpire cannot give the next batter a strike to start off his at bat.