I think we can all agree that a card that has not been seen is random. Therefore, when you calculate outs for a flush draw, you have 9 outs. So burn cards shouldn't matter.

I can burn 1 card and show the turn/river or burn 8 cards and show the turn/river. The probability is still the same, so I don't understand people who complain "mis-burned" cards, or "mis-dealt" cards.

My house: As long as the card is shown, leave it.