Got one for you
 

I'm working the plate. We have one out and runners on 1st and 2nd. Strike 3 is called, but the ball is dropped. I scream strike 3, the batters out. The runner takes off for 1st and I still scream BATTER is out. Coach calls time and ask's why his runner can't run to 1st. I told him that he is struck out. He ask me why, can he run if the catcher drops the ball on the 3rd strike. I said yes he can, but if they are 1 out or less and 1st base is covered, the batter is automaticly out. He then told me that he coaches his players to run down on a drop 3rd strike. I told him that I don't know how its coach, but how it's umpired, we called the batter out. Question, Should I tell everyone that the batter is out or should I let everyone figure that one out?

I believe this is in the FED rule book to announce the batters out. I wouldn't scream it, however. If batter runs and runners advance it isn't against the rules. Just make sure you take batter off the base if he acquires a base. I'm sure the coach is okay if his runner is forced at a base in the same situation.

Let the defense figure out what to do. Just call it when it happens!:D

As Mr. Tyler indicates, you should "forcefully state" that the batter is out, then whatever happens, happens.

Call the batter out one time. If the catcher is smart, his next throw will be to third. If he is not, he needs to be coached better.