[Lottery Larry]

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So I'm playing at one of the three tables, and there is a friend of a friend dealing who deals out the flop, turn and river all at once face down, before the the pre-flop action is over.

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I've done this occasionally, as the host, so I can abdicate my dealing duties in a hand I'm not in and deal with floor/chef/hosting duties. Since I regularly check my decks after the game nights, I'm not TOO worried about a random hand exposing marked cards. I don't do it regularly.

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Well, there is a hefty raise and one caller. Then someone else, not in the hand, mistakenly mixes the mucked cards with the burncards and pre-dealt hand.

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So, action is still preflop and the board has not been exposed yet.

If there was no way to reduce the amount of mucked hands contaminating the rest of the stub, I might go with using the virgin stub only. Generally, I'd prefer the reshuffle/redeal of the hidden cards... but there can be NO risk that someone in the hand saw a mucked hand.

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who is running the thing says to just deal off the deck and check it down.

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Possibly the worst decision that he could make. He had to make a decision, but he didn't think that checking down thing through carefully.

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And what rules could be put in place to prevent this kind of thing in the future?

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No matter how many rules you have, something always comes up in the gaps. It's best to make reasonable decisions that impinge on the normal play of the game as little as possible.

Mistakes happen, especially in more casual home games.