The Two Towers was easily a better movie than Return of the King; the reasons why - the battles were more impressive, the last 30 minutes weren't an exceptionally long procession of goodbye scenes, and finally, less attention was given to the annoying and touchy-feely Hobbits. Perhaps, one particular individual would disagree with me, but Mystic River was also flat out better than Return of the King.
Someone earlier mentioned the futility of awards shows covering such a wide range of movie genres. I would disagree because the Oscars and the Golden Globes are both shows that (in theory) are supposed to measure the quality of filmmaking in a given year. Best Picture is supposed to be given to the best film in a year, and that can be measured by observing all of the creative and technical aspects of films. For example, Return of the King easily had the best special effects of any film in this year. The detail of the costumes and sets were simply amazing, and the soundtrack was pretty good too. So, Return of the King already had a lot going for it in the technical senses.
The acting was quite good among Viggo Mortensen, Ian McKellen, Miranda Otto, and various other members of the cast, but I'd argue that the plot was more original and the acting was better in Mystic River. Mystic River may be a totally different genre than LOTR, and LOTR might be a classic series of books, however, as far as films go, I'd argue Mystic River was easily better. The themes behind LOTR were interesting, but they weren't anything particularly original. Most of the ideas presented in LOTR follow the typical and timeless themes of the epic. Good vs. Bad... Power vs. Humility... and many countless others. While these themes are important and easy for anyone to relate to, Mystic River tackled many issues that are both original and not so readily accessible. Vengeance is basically the core of that movie, but it shows just how insidious a reaction it really is.
I might be going out on a limb here, but seriously, the most important part of a movie is its message. If the message is something that everyone already knows, then it's not a very powerful message. The movies that are the most influential make you think. No one can dispute the evil of Saruman or Sauron, or the good of Gandalf or Stryder. In Mystic River, everyone is a shade of grey on the good/bad scale, and life itself is far more like the shades of grey idea than the black-and-white/good-and-evil ideology so often seen in fantasy. If you've seen Mystic River, you'll know what I mean when I say that you'll find yourself debating the justifications of each character's actions. Sometimes, good and evil aren't so explicit, and movies that continually remind us of this fact are usually the most innovative and impressive. Mystic River may not have won Best Picture, but it's easy to see why Sean Penn and Tim Robbins won what they did. I'd have to disagree with Steve that, in fact, Return of the King won Best Picture to avoid a crying jag by the most fanatical LOTR fans....
Unfortunately, the Oscars and many other awards shows have become political affairs. Instead of the best movie winning Best Picture, the most popular will win. The best example of this is when Titanic won Best Picture in 1997. The majority of the industry agreed that L.A. Confidential was a far better movie, but it didn't do as well in the box office, so Titanic won. Other times, certain actors, actresses, directors, or producers will be rewarded for their connections to Hollywood. Finally, there are cases when the Oscars are blatantly political; I have no doubt in my mind that Denzel Washington won Best Actor for his performance in Training Day and Halle Berry won Best Actress for her performance in Monster's Ball both in 2001 due to their ethnicities. Don't get me wrong: Denzel and Halle are very good at acting, but I'd seen better performances by both of them in other movies. There were better performances in other movies that year as well, but I think the Academy was trying to shed its image of being a mostly white awards show by awarding both of them. Anyone can see that the majority of winners of Oscars are white. I'm not saying there's anything wrong with the choices of winners each year, but you do have to remember that Sydney Poitier was the first minority actor awarded Best Actor back in 1964. I suppose the Academy had decided enough time had passed to repeat this event, and ironically, Sydney also won something that night.
