I didn't put down the players hands because I didn't want this to influence the discussion, but it ended up being pretty fun.

The hands were Ah-7d, As-Ks, and Ad-Ac. The flop was 8-5-3 with 1 spade. the boxed card was the 4 of diamonds, but when discarding that card the 7 of spades ended up being the next card which opened up a flush draw for A-K spades and giving A-7 one of the 7's he needed to make trips. After the next burn came off the next two boxed cards were both 7's, essentially killing A-7's chances of hitting trips. We neevr exposed the river card as I made my decision on seeing that there were so many boxed cards.

I do like the suggestion of only misdealing mid-hand if action is not complete, but continuing the board if all action is closed (because of 1 or more all-ins). Only problem I have with that though, is this worst-case scenario: If you are dealing Omaha, you get two all-ins pre-flop, you burn the top card and discover a boxed card there. You discard that, put the flop, and then discover 3 more boxed cards, discard all those and then discover 3 more boxed cards. Now you'd have to go into burn cards to find enough live cards for the board. I'm not saying it's probable, but it does show that there must be a cutoff on acceptable number of boxed cards no matter what stage in the hand you are in.