The shooting script for Two Towers had Arwen showing up at Helm's Deep and fighting in that battle. They filmed a lot of that but ended up not using it. I think most of us would agree that was the right choice. It was better for Jackson to err on the side of the book, where Arwen doesn't play a major role. Besides, at least in the extended versions of the last two movies there are periodic Arwen appearances.
- The physical manifestation of the Eye of Sauron in ROTK. I know that Peter Jackson agonized over how to visualize the idea that the Hobbits could feel Sauron's inner eye focused on them. But I don't think what he went with worked. In Fellowship, when Frodo puts on the ring and we see the world as he sees it and the visualization was so, SO perfect. But in ROTK, the eye sitting on top of the tower like some sort of Spotlight Of Evil™ just looked silly, especially when the tower is collapsing and the eye is looking about in horror. THE EYE IS NOT SAURON! But most audiences walked out thinking it was. I think this could have done better.
What would you have done instead? Originally a physical embodiment of Sauron fought Aragorn at the Black Gate - that was what they filmed. Some elements of that were used in some reaction shots they left in that part of the movie. Later they superimposed the cave troll instead because they didn't think the idea worked. The problem is that Sauron in the books is a rather nebulous concept to begin with, something that takes a lot of explanation by Tolkien to get across.