Here's what RROP says about it. Interesting that it states that if there is any action on the betting round, rather than substantial action, then the action stands. Also, it recommends putting one of the burn cards back on the deck and using it as the next burn card in order to stay with the original river card.
Quote:
16.If the dealer fails to burn a card or burns more than one card, the error should be corrected if discovered before betting action has started for that round. Once action has been taken on a boardcard, the card must stand. Whether the error is able to be corrected or not, subsequent cards dealt should be those that would have come if no error had occurred. For example, if two cards were burned, one of the cards should be put back on the deck and used for the burncard on the next round. On the last round, if there was no betting because a player was all-in, the error should be corrected if discovered before the pot has been awarded, provided the deck stub, boardcards, and burncards are all sufficiently intact to determine the proper replacement card.
