I've railed about this back in the old LOTR forum, but I'll reair my complaint again here.
By far the biggest complaint I had about the LOTR trilogy was the role of Saruman. In the book, Saruman is corrupted by the ring. I guess one of the messages of the book is that the more powerful and 'wise' you are, the more susceptible you are to corruption by the ring (and perhaps corruption in general). Saruman is so wise and powerful, he gets corrupted even without physical contact with the ring! He is corrupted because he studies ringlore so deeply, and in the end decides to wield it for himself and become master of Middle Earth.
In the movie, they made his mind-boggling betrayal of Middle Earth into just a cowardly, Machievellian decision. He figured Sauron would win, so he wanted to brown nose the Dark Lord. The Saruman from the book would have preferred to die a painful death rather than to bow to anyone, Sauron included. He was rising up AGAINST Sauron, not becoming his willing lieutenant. I recall a dialogue in the LOTR (though I don't recall who said it) where someone regrets that Isengard and Mordor could not be next to each other so the two armies could smash each other to smithereen...but then it is noted (I assume by Gandalf) that the eventual winner would emerge even more powerful.
By unnecessarily changing this aspect, I felt the filmmakers 1) didn't do justice to the character of Saruman from the book and, 2) missed an opportunity to reinforce yet again the power of corruption in the ring.
Related to this is my secondary complaint. My understanding from the book was that the ring COULD be used by anyone powerful enough. They COULD use it to overpower Sauron and become the lord of Middle Earth. The only trouble was they would become corrupted in the process and become dark lords themselves. In the movie, it is claimed, NO ONE can use this ring besides Sauron. The ring only has one master, the ring and Sauron are one and the same. If so, then why does Gandalf ask Frodo to not "tempt" him with the ring? If he can't REALLY use the ring to become powerful anyway? This turned it from a REAL temptation to just some illusion.
