Is this a miss deal or does the hand stand (Texas Hold'em)?

Sort of both. Player 2 is correct, it was a mis-deal. The hand should have been redealt so that everyone gets a fair chance. BUT, the hand was concluded, and player 1 announced his straight, with player 2 announcing his 2 pair. Player one started raking in the chips, the hand is over. Any problems can be solved during the hand, not after money is being exchanged. That would get you shot in some of the places I've played in.

Player 2 is right. It's not called a misdeal, per say, even though the dealer of that hand did mess up by putting an extra burn card. If possible, the best way to rectify the situation is to recreate it. So you'd pull back the "river" which wasn't really the river and place it back on top of the deck. That card never really came. Then you'd walk it back from there correcting the action. So Player 1 would not have got his straight, but player 2 would probably not gotten 2 pair either.

If there was no way to recreate the situation to correct it; the cards already too messed up and ready for the next hand, the ruling would be that both players get their chips back. So yes, player 2 was right.

It's not a misdeal, if only one card was accidentally exposed as hole cards were being dealt and the correct procedure was used from that point.

The correct procedure is to continue dealing, as if the card had not been exposed, until all players have their hole cards. The exposed card should then be replaced with what would have been the first burn card, and placed on the deck to take that cards place. The only circumstances that would be considered a misdeal is: 1) first card dealt to the small blind, big blind or the button are exposed, or 2) more than one hole card is exposed.

The burn card should never be "burned" until all action of the betting round is complete. If this rule is followed, along with placing the burn cards in a place where they can be accounted for, this problem could have been avoided. The purpose of burn cards is to conceal the next community card from players that could possibly benefit from marked cards. If it's burnt before the action is complete, it defeats the purpose of having it.

Chips should only "go back" in the event of an actual misdeal, otherwise substantial action forces the hand to continue and be played to conclusion.

player 2 is correct, since the dealer burnt an extra card it is a misdeal, and the last card on the flop should have been burnt for the turn...the board and burn cards should be removed and reshuffled, and the board should be redealt

I think its a misdeal, but should have been caught probably in when the cards were flopped before the river cards.

The hand was misdealt.