Where can I get advice/rules as to how to handle dealer mistakes for some of the lesser known games?
We play Archie, triple draw, and drawmaha in our home game and I can't find what to do when a dealer exposes a card.

Examples:
Triple draw. Dealer is dealing the original 5 cards. One of the cards flashes/gets exposed. Does this get shuffled back into the deck now, or do we wait until we're out of original cards and are re-shuffling. Does the rule change if it happens during a draw?

Drawmaha -- The river card gets prematurely exposed before turn action was completed. Does it get shuffled in with the stub? Do you included mucked hands? Do you include burn cards? The problem with Drawmaha is that there are so few cards left at the end that the exposed card can be one of a few that would be shuffled back in.
What if the turn is prematurely exposed?

RRoP doesn't have specific answers for those games.

Let me know if this should go in the Casino/Cardroom Poker section

Yeah, I think this might need some mixed game expertise I'm not sure we have here. I'd try there, but I'll also leave this open in case one of our old timers who used to run mixed games catches it.

I think this first one is pretty easy - it shouldn't be shuffled back into the deck, it should be used as the burn card, just as an exposed card is treated in the initial deal in holdem.
Eventually it would be shuffled back in if you run out of cards.
Some old lowball rules say that the player keeps the exposed card if it is a wheel card, but that generally isn't followed in casino games anymore.

It should never happen during a draw, because the cards are supposed to be slid across the table gently to each player, not pitched like in the initial deal.
So I don't remember every seeing this happen in a casino, but I would imagine it should also be treated as the next burn card, and again shuffled back in if there is a reshuffle.

I wouldn't call myself an expert on these procedures, but I have played a pretty good amount of triple draw games in casinos and a little bit in home games. I've played very little Drawmaha, as I hate the game, so I can't really help you with that.

On the deal, the exposed card becomes the next burn card. If two cards are exposed, then it's a misdeal. As to the draw, I couldn't find anything in the TDA but it does say in Stud that if 7th street is exposed and no action has occurred, the player gets a new card. The exposed card would go into the muck.

The correct (and mathematical) way would be to put the exposed cards into the muck for non-hold'em games. However, TDA rules say they should be shuffled back into the stub only (no muck or burns) and redeal the river. If an early turn, the river card would be the new turn and then you'd shuffle the stub. If you have two cards remaining in the stub when putting out the river, you can use the last card for the river. If you only have 1 card, you'll mix it with the muck, cut it, and use it for your burn and river cards. High limit games will also pull in the burns for this procedure. Low limit players are too dumb to know what street they are on so the burn cards stay out for them.