[emaxos]

..I very often tell spectators to shut up until they learn the rules....

Perhaps "shut up" was too harsh. When I am outside the fence watching games, I have tried to correct spectators in a tactful, informative manner about the rules. As a coach, I'll wait until after the game if I feel one of the fans is misinformed.
Either way, I do it quietly.
If I'm announcing a game, I try to explain certain rulings that may not be widely known. I recall explaining IFR, obstruction, interference and the basics of DP/FLEX.
Several umpires have thanked me for doing that as it lessens the comments.