In the extended edition, the Mouth of Sauron makes a brief appearance. His physical appearance can be seen as unsettling (notably for younger audiences) as he has a grotesque mouth that has the lips cracking, flesh rotting, and teeth decaying. He often turns his head erratically and showcases his decaying teeth often, with his lips retracting greatly.
Gollum's transformation in the opening scene of the film is deeply disturbing.
The long, violent battlefield sequences are quite scary as the heroes are always under threat of death or serious injury.
A trio of characters journey through "The Paths of the Dead" and encounter ghosts.
Frodo gets attacked by a giant spider while Sam battles against it and it's very intense (these sequences can especially frighten those who suffer from arachnophobia). The spider also moves very quickly which makes the scene all the more intense
The Witch-King scenes may be frightening for some.
Two of the characters descend into violent madness. The first of these is marked by a transformation into a creepy creature. That scene is particularly intense.
Gollum's appearance and voice can be frightening.
This is a rather violent movie but not much blood/gore is shown. It has a fantasy overtone to it.
The ending of the film is emotionally intense. It is one of the most emotional scenes in motion picture history to some.