Since I've only seen RotK once, i was going to let you off easy. But, you asked for it:
Points of character development throughout RotK (note, not in order of appearance or importance):
1) Theoden recognizing Eowen as his daughter who he loves, who he has not treated as such to date. He's been a good king, but until now he hasn't been much of a father for her.
2) Aragorn (or Elessar by this point if you prefer) facing the weakness of men when he sees the eye of sauron. The moment he's been dreading for all this time, and he turns around and attacks. He does not falter. IMPORTANT character point.
3) Aragorn facing the dead (i know it didn't happen in the books, they just picked up the banner and moved on). However, this is illustrating how he's taking up the burden set down by Issildur. Yes its different than in the books. Yes its very symbollic. Yes, its just as good as the book.
4) Watch Pippen closely in Minas Tirith. He is faced with what looks like a hopeless battle. His reactions before and during the battle are much different than the hobbit from the shire, or from Orthanc. He has changed.
5) Denethor at the pyre. Even as he plans to burn himself as the heretic kings of old did, he is shown his own folly. Gandalf holds the mirror up to him as it were. In the moment that he realizes what he has become, he throws himself, flaming, from the top of the city. The haughty, gluttonous man that was the steward of gondor changes in those few moments.
6) Sam handing back the ring in Cirith Ungol. He is tempted, he is tested. He now knows exactly what Frodo feels. Sam is shaken, and changed from his contact with the ring, however short it was. If i remember right, Sam is offered a chance (in the appendix) to sail to the undying lands because he carried the ring if only for a while.
7) Frodo is finally corrupted by the ring. After having made it all the way to the Cracks of Doom, he finally breaks. BIG CHARACTER POINT.
8) Bilbo at the very end. He no longer really wishes to see the ring. Under the care of the elves, the hold the ring had on him has diminished. The shadow over his soul has passed, and he is now the hobbit he once was.
9) Frodo leaving Sam. After devoting his life to serving Frodo, Sam now stakes out a new life of his own. He becomes a whole person.
10) Aragorn marries Arwen. Another case of a shadow passing over his soul, the doubt in his heart is gone. He can now freely devote his life to his love. Now he is happy, no longer troubled as he was in the marshes (in Fellowship) or on the ride to Edoras (in the Two Towers).
These are ten examples of character development in RotK. Most of them are pivotal points in that characters life, for better or for worse. The movie includes them, and does a damn fine job of conveying that info to the audience.
(note: i've only seen the movie once. Once the DVD comes out, I'll be able to give you more examples
.)