Apart from being able to really follow the book (a major criticism of the LOTR trilogy, as major plot points were completely eliminated or drastically altered; see: cleansing of the Shire, the Siege of Minas Tirith being reduced to a several-hour battle, the erasure of the Field of Cormallen scene and Aragorn’s coronation, the erasure of the Black Breath subplot, Denethor’s Palantir, etc), doing the movie as a trilogy allows him to explore the White Council and the expulsion of the Necromancer from Dol Guldur. It also permits a longer flashback for Gandalf when he found Thrain in the Necromancer’s dungeon and received the map of the Lonely Mountain. Finally, it allows a bit of fill-in for the space between The Hobbit and the LOTR series, with Gollum’s journey to Mordor, an introduction to the Rangers, and so on.
I thought the most egregious change in the story was the rather silly misuse of the Dead. Really, green glowing invincible warriors? Why didn’t Aragorn just march on Mordor with them and get it over with?
Also the great misuse of Faramir’s character. In the book he was one of the most admirable characters. Not to mention the way the hobbits somehow crossed the Great River twice without noticing it.