Continuity Gaffe: In the Two Towers Merry’s wound on this forehead switches sides upon entry into Fangorn and stays on the other side for a couple of shots then jumps back to the correct side again. Watch the ‘Medicine’ scene, then the ‘encampment’ outside Fangorn, then the escape from the Orc and finally the conversation with Treebeard.
The only one I noticed by myself was in FOTR:
During Boromir’s big emotional death scene he has one hand clasped around the back of Aragorn’s head. But the hand keeps disappearing every time the perspective shifts from Boromir’s face to Aragorn’s.
That was done on purpose. On the EE commentaries, the actors mention that the scenes are being flipped. You can tell when it happens by looking at the clasps on their cloaks. Jackson mentioned on the director commentary that he would flip scenes anytime he thought it looked or worked better to have the actors looking the other way.