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.
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.
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.
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.
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 Theoden. 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.