Oh, man, I know I'm gonna get flamed for this, but I must respectfully disagree: while a good movie, I did not find Minority Report to be a great movie.
In brief detail...
(SPOILERS AHEAD)
+ As I feared from the trailers, the colors were FAR too faded, the shots far too blurry. There's no sense, I think, in lingering on the special effects, but showing them clearly makes them more believable. It is, I suspect, why 2001 and Star Wars: A New Hope continue to amaze audiences more than, say, Blade Runner; unlike the latter, the first two don't try to hide their effects in murkiness.
As an aside, I thought the "fuzzy" scenes in Lord of the Rings were - while a fine idea - simply overdone. To apply it to EVERY flashback, Rivendell, AND Lothlorien seemed a bit much. MR was much, much worse in this department.
+ The "look" of the future flip-flopped too quickly, and was too quickly associated with how the audience was supposed to react. There was "The Future (TM)", with its the magnetic cars, rocket packs, and the Pre-Cogs; then there was "next week," with its townhouses, farmhouses, and unchanged appearance of historic Washington, D.C. (What, no giant freeway hovercar tracks near the Washington Monument?) The two looks were completely separated, and it always seemed the scary chase scenes and intellectual discussions were (mostly) for "The Future (TM)," and the emotional, heart-wrenching scenes were set in "next week."
I thought A.I. suffered from the same problem, but at least that movie had an excuse, namely what I thought was an innate incompatibility between the styles of icy Kubrick and fuzzy Spielberg.
This seemed particularly noticeable after Attack of the Clones: between the odd styles of fashion and the ever-present flow of flying traffic, you always new you were on the futuristic capital city-planet of Coruscant.
(While I'm on the subject of comparing the two, I noticed a remarkable similarity between AOTC's conveyor belt scene in the droid foundry and MR's scene in the auto factory. Which is fine, but the fact that the machinery transformed into a car around our hero - a car with a full gas tank/power cell, rolling conveniently into an unguarded, open garage door - to be a bit hard to swallow. It took me out of the movie for a moment. Not a major complaint, but worth noting.)
(I know that moment was supposed to be amusing, but - like many other moments in the movie - the comedy seemed a bit forced; the only time I remember REALLY laughing in humor, rather than in disbelief, was the "eye-rolling" scene.)
+ Speaking of things that didn't work, what was up with the mad scientist lady? Or the wooden balls with the victim's and killer's name?
(And was I the only one reminded of the "pinball" counting sequence in Sesame Street?)
+ As with most movies involving time-travel or predicting the future, MR seemed to be making up its own rules as it goes along.
As a minor point, I thought the Pre-Cogs didn't tell the future beyond acts of murder - and that they were useless on their own. Of course, Agatha was able to break both rules to help John on her own.
Beyond that, the rule was that only premeditated murder triggered an alarm days in advance. But John's murder certainly didn't seem premeditated - considering he didn't know who the guy was (or was supposed to be) until mere moments before the fateful moment.
As a MAJOR point, how exactly was the set-up executed? John seeing the murder is what triggered the events that led up to the confrontation. That's a bit paradoxical, and it begs the question: how'd the bad guy set that up? It seems like the ONLY thing he could have done was told the guy to get a hotel room, pretend he was not who said he was and show up at such-and-such time. But that doesn't seem like enough to trigger the Pre-Cog's warning system.
+ Like A.I., there seemed to be at least one too many endings. It seemed like it could have ended in the hotel room, when John was dropped into the vault, and in the ending proper. That many false endings is not a way to end a movie.
+ A couple plot contrivances, including (but probably not limited to) the convenient secret back door to the "Temple;" the fact that no one bothered to delete John's clearance to such highly restricted areas; and that John's wife was able to get him released, cogent, and up-to-speed in so very little time.
+ The ending itself. Essentially, the good guys won because of a slip of the tongue on the part of the bad guy. To have the good guys intentionally set up the bad guy (as I thought was going on, until John's wife seemed to be that genuinely dense) would have been cool. To have the courage to end the movie on a dark note (the original Planet of the Apes) or an ambiguous note (the director's cut of Blade Runner) would have been cooler.
The ending, the pull-back from a happy moment of peace reminded me of the end of The Shawshank Redemption. In the case of the latter, there was no "deus ex machina" at the end; rewatch the movie, and you'll the pieces fall into place. It feels like the happy ending was more properly earned.
I fully admit, the movie is quite cool: the premise is intriguing.
(I thought the same of A.I.'s premise. As presented in the movie's opening scene, the question was whether a robot that acted human could still be loved. But since the robot NEVER really acted like a real child, the premise was never addressed.)
The opening sequence rocked, particularly the computer interface and the race against the clock. The need for John to change his eyes was very good. The "spider" scene was riveting. And the fact that Cruise's eyes went from light blue to dark brown was a lovely touch.
That said...
Blade Runner had a more consistent look for the future.
The Star Wars prequels have a much more dazzling view of a futuristic city.
The Fugitive was a better chase movie with a more satisfying conclusion.
The Indiana Jones movies had a better sense of humor.
And I've seen episodes of Red Dwarf ("Future Echoes" in particular) that dealt with knowing the future with a LOT more internal consistency.
Like the coolest thing ever! 
I'd love it!
