I go all in on the turn, the river gives me a full house which beats the other players three of a kind that he showed, I slap my cards down face up to show and one flips itself over and goes into the muck pile clearly on top. How should this be ruled?
All in rules are fairly standard and ubiquitous across wherever you play. From WSOP to TDA it's pretty clear as long as a hand is 100% retrievable and identifiable the hand will be ruled as not dead. Of course you will always get some deviation from this, it's important that floors are people and were not there at the time of things happening and are often trying to do their best, but any where that is going to kill an all-in hand that has been clearly shown is somewhere you should not be playing.
Cash is a different story as often it can be simply down to the table agreeing and that's enough. Many times these situations can be resolved without floor coming in for cash.
In your case you said you have slapped cards face up and are all-in. Hand is live, as everyone knows your cards, you're all-in. An all-in hand that has been exposed cannot be deemed dead, unless a stronger hand is shown. In this case it's irrelevant that the cards have touched the muck. If however your card didn't expose and ended up deep in the muck, well sorry, you'll probably be ruled to play with the one card exposed. If the card didn't expose and want on the top of the muck and everyone knows that is your card, i.e. 100% retrievable and identifiable then you should be fine.
Although organized events like WSOP may allow cards in specific situations to enter the muck and rely on an official to determine which cards came from a player's hand, every smaller-scale game I've ever played is run by the opposite rule: Once a card hits the muck it is deemed dead.
The primary reason for this is simple: It prevents any possible ambiguity as to which cards were in one's hand.
The secondary reason is that this rule helps keep the game friendly and penalizes players if they get unruly and throw their cards.