Umpire wrong. How to handle?

[just another ref]

We had a similar situation earlier this year. PU forgot momentarily which field he was on, he had been calling the younger kids more often this year. He yelled, "Batter's out! That's not a foul ball! It hit my shin guard!" Fortunately my guy kept running (surprise) and was safe at first without a throw. I asked later what if my batter had stopped when he heard the out call and was told he would have been awarded first base. Is this right? Conversely, the defense in this case could have argued that their catcher stopped when he heard the call. (I don't think he really did, but it would have been worth a try ) What is the deal in baseball about a black and white (correctable error?) case such as this, or an infield fly call, but, oops, there was no runner on first, etc. Want to be prepared next time. Thanks.