Continuity mistake: In the second half of the film, Frodo has a scar on his lower right cheek, close to his chin. Many times throughout the rest of the film the scar changes position and size on his right cheek. It also appears on his left cheek in flipped shots (most obviously on the slopes of Mount Doom when Sam is cradling his head).
Continuity mistake: Legolas sends an arrow directly to Grima atop Orthanc, and as Grima starts to fall back the arrow is quite visibly well below the coat's fur. However, when Grima actually hits the ground, the arrow is now higher up, protruding from the fur. (Extended Edition.)
Continuity mistake: As Sam lay sleeping, Gollum sprinkles lembas crumbs on Sam's right side. 1st shot, the grey blanket completely covers Sam as Gollum begins to sprinkle it. 2nd shot, the blanket is at Sam's shoulder with a just a bit of cloak and sleeve showing. 3rd shot, the blanket is completely covering Sam's shoulders as the lembas is shown only on the blanket. Then Sam stands and the blanket is now on the ground (as mentioned in another mistake, there are no crumbs at all when he stands). Later, when Gollum accuses Sam in the 'framing' shot, the lembas crumbs are shown on Sam's cloak even though it was the grey blanket Gollum sprinkled it on earlier.
Trivia: When Gandalf is talking about the gathering of the armies of Sauron, the next shot shows the Corsairs on a ship. Walking there from right to left is Peter Jackson in a cameo as a Corsair pirate. In the Extended DVD, at the start of Disc 2, he is actually pierced in the chest by Legolas' arrow and dramatically dies!