By rule, umpire's interference only applies when the umpire is hit by a fair batted ball BEFORE it has passed an infielder, or when he interferes with a catcher's throw in an attempt to retire a runner. Anything else that an umpire is involved in is a live ball and play continues. It is not umpire interference, its a mistake. The coaches won't like it but the play stands.

If an umpire makes a mistake on a call and his action creates a dead ball situation, he should not reverse his call and try to ASSUME what would have happened if he had not "killed" the play.

Here's an example: if the batter hits a pitch and it hits the plate and then goes into fair territory. It is a fair ball by rule. However, if an umpire yells "foul ball" when it hits the plate, he should stay with that call. The same as if he made a bad judgment on a fair/foul ball that hit near the line. Once an umpire makes a call which creates a dead ball situation, he should not reverse the call, no matter how bad it was. He could reverse a call in which the original call was "fair", because you can put everyone back where they were before the call. But, when you kill a play, you can't guess as to what would have happened, had play continued.