Lord of The Rings: Fellowship of The Ring - Ventriloquist Frodo
First go to the beginning of the movie at Bilbo's party. There is a short scene where Frodo is dancing. He sits down next to Sam and says, "Go ask Rosie for a dance!" Sam says that he wants more ale. He gets up to get it and Frodo pushes him towards Rosie and says, "Oh no you don't." Watch his mouth when he says this. The camera changes angles so watch carefully. Frodo's mouth does not move.
Now skip to the scene where the cave troll is terrorizing the Fellowship in Moria. At some point he grabs Frodo's leg and drags him along the floor. Frodo grabs at some rocks and shouts, "Aragorn! ARAGORN!!!" Upon closer inspection you will notice that his mouth is not moving when he says this. In fact, it is clamped shut.
I love these movies, even with all their slipups :-)
I have the Extended Edition - it might be on the original as well