There are tons in LOTR...
In FOTR, When Frodo and sam run to look at the Wood Elves, at first, Frodo is to one side of sam, and then they film from behind, and they switch sides - only to switch back again, when filmed from the front.
This is pretty funny...When aragorn runs up to boromir as he is dying, he jumps over a bunch of orc bodies...I'm not sure if its a blooper, but one of the 'dead' orcs lifts his head up to watch the scene.
