The name of the wizard of Isengard fluctuates between "Saruman" and "Aruman" throughout the movie.
Celeborn's name is mispronounced ("Seleborn" instead of "Keleborn").
"Minas Tirith" is consistently mispronounced as "Mine-as Tirith" rather than "Min-as Tirith".
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.
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.
The same close-ups of Legolas firing his bow and then running appear twice each during the Helm's Deep sequence.
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.
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.