Continuity: After Gandalf returns to the company of Aragorn, Legolas and Gimli as Gandalf The White (wearing a solid white outfit), he accompanies them to the castle of King Theodin. When the group is walking up to the entrance, Gandalf is suddenly shown in his original grey cloak and blue hat. In the next shot, he is wearing all white again.
Continuity: In the first shot of the orc attack in Moria, Legolas' bow is tall with spiral tips (which he uses throughout the movie). In the very next shot, two seconds later, it is much smaller, with the regular curved tips of a straight-limb longbow.
Continuity: The night Boromir tries to persuade Frodo to lend him the ring, the moon is behind Frodo, but it is also behind Boromir as well.
Revealing mistakes: In many, many shots throughout the second half of the movie, the blond Legolas has dark hair. The actor who played Legolas in the live-action footage on which the movie was based clearly had dark hair, and these shots were insufficiently fully converted into animation.
Revealing mistakes: The Dwarf Gimli is almost as tall as the human and Elven characters in this movie. Presumably the actor who played him in the live-action footage was insufficiently short, and it was considered impractical to shrink him in the rotoscoping process.
Errors made by characters (possibly deliberate errors by the filmmakers): The name of the wizard of Isengard fluctuates between "Saruman" and "Aruman" throughout the movie.
Errors made by characters (possibly deliberate errors by the filmmakers): Celeborn's name is mispronounced ("Seleborn" instead of "Keleborn").
Continuity: The same close-ups of Legolas firing his bow and then running appear twice each during the Helm's Deep sequence.
Errors made by characters (possibly deliberate errors by the filmmakers): Saruman is called "Saruman the White" and "Saruman of Many Colors", yet throughout this movie he is dressed entirely in red.
Revealing mistakes: When Gandalf is revealed to be alive again, he jumps up onto a rock. His cloak becomes wrapped around his staff and has to be disentangled - clearly a mishap carried over from the live-action footage.
Errors made by characters (possibly deliberate errors by the filmmakers): "Minas Tirith" is consistently mispronounced as "Mine-as Tirith" rather than "Min-as Tirith".
Errors made by characters (possibly deliberate errors by the filmmakers): Gandalf and Aragorn pronounce "Edoras" differently.
Continuity: Whilst Gandalf is talking to Theoden and Worm-tongue in Edoras Gimli's hood appears and disappears as the camera angles change.
Continuity: In Rivendell when you first see Bilbo he is stood reciting poetry, while the other four hobbits walk into the room. In one frame you see Frodo sat in a corner playing a harp, then it returns to him entering with the other hobbits and it is an elf playing the harp.