I was playing 1/2 in a card room last week when an interesting situation came up which had me stumped.
*8 handed game, 3 way action on the turn;
*first and second position check, button bets $50.
*First position goes all in for $71 total and second position calls.
*The action is back to the button to either fold or call $21, but the dealer overlooks this and puts out the river.
*Floor comes over and instructs the dealer to take back the river and tells the button the action is on her.
*She calls
*floor tells the dealer to shuffle the river back into the deck;
*the dealer starts doing this when he realizes he also picked up the muck and combined it with the rest of the deck.

***Now what??????

Finish shuffling, cut, no burn, and put the new river out.

Burn and Turn, assuming the burn card on the river is now in the deck. Action is first position.

What else can be done? In theory, nothing as changed because to the players remaining in the hand, all of those cards are possible to come out on the river unless a card was exposed.

deal river after shuffle seems right here.

deal river, poke fun at the dealer for his mistake

The thing you never, ever do is say a gol-danged word if one of your mucked cards shows up.

I understand the rational of just shuffling and dealing MOST of the time when this situation arises. However, I felt that this situation was different as the button only had 2 options, call $21 or fold. Being that there was almost $200 put in the pot on the turn alone, the button calls almost all the time.
What about this -- when the dealer puts the river out by mistake it is taken back and the action is on the button. The button calls (or folds, it doesnt matter) thinking there will be a new river card.
Then when the BIG mistake is uncovered, why not just put the true river back out there?
The point I'm making here is the button did not rely on any information gained which was unfair; when she made her decision she thought she was going to see a random river. When the mistake is uncovered, especially when the button would just about never fold in this spot regardless, what is the harm in avoiding the mess of adding the muck into the deck and just putting the true river back out there?

Did you attend the Gober Lindsey school of poker dealing and skate board repair?

because that's unfair to the caller. the information everyone at the table had there was that there was going to be a random card dealt as the river, but she's the only one with a decision as you said so it seems like bait and switch almost. what would be the point again?