Spoiler Level: High
Does this count as science fiction? Well, it's the story of Operation Jedi, a special military program where a unit is trained to develop their psychic abilities, so yeah, I'd say it counts.
Except it's only partly fiction.
It's a dramatization of a real military program that actually happened, called the First Earth Battalion, fictionalized here as the New Earth Army. Jeff Bridges' character Bill Django (based on real life Lieutenant Commander Jim Channon) has a goal of changing the military into something new, a force that turns aggression aside before the need for combat arises, using new age attitudes and unlocking the inner abilities of the mind.
George Clooney plays Lyn Cassady (based primarily on Glenn Wheaton), a retired soldier from the program who meets Bob Wilton (played by Ewan "Obi-Wan" McGregor, and based on Jon Ronson, the writer of the original book). The two meet in Kuwait and end up heading into Iraq together, giving Wilton the chance to learn all about the New Earth Army program.
And there's where the fun really begins. Cassady's flashback scenes to the New Earth Army program are all from his perspective, so we see them all as successful. And you think, wow, this guy is really on to something here, this is incredible. Then you see him try to apply it in the real world and you think, wow, this guy is completely delusional. And that's where the humor comes in.
If I can get a little too personal for a review and speak to my peeps in the fanboy community here... we know these people are real. We've met them. Hell, some of us are them. I think if you did a survey, you'd find most of us in fandom are at least open to the idea of psychic abilities being real, with a sizable percentage believing yes, absolutely they're real, and a somewhat smaller percentage going as far as to say they have them. I've known quite a few in my time who believe they have psychic abilities, and although one or two them were a little unhinged, the majority were very well balanced, educated people.
Personally, I have to put myself in the open-minded category; I've always been a believer in the persepctive that "there are more things in Heaven and Earth than are dreamt of in your philosophy," and I've seen a few things over the years that have made me raise an eyebrow in wonder, but my inner skeptic keeps me from being a full-on believer. I've never seen anything that could be repeated per the scientific method's requirements. As Michael Shermer pointed out in his wonderful book Why People Believe Weird Things, we tend to remember the hits and forget the misses.
And to be frank, the concept of psychic abilities is something that people in our community really want to believe. I don't mean that in the slightest derogatory way; the idea that there's something special, some great potential inside us that can be unlocked is naturally appealing. And unlike starships or dragons or vampires, where it's easy to point to the details of it and say "it doesn't exist," this is a concept that resides inside the human mind, so the idea that there's someone out there who has mastered it is nearly impossible to disprove.
And that appeal is where the humor lies in this movie, especially for those of us in the fandom community. Is this guy the real deal, or someone who's just bought too heavily into the fantasy? We want to believe in him, but man, sometimes you just can't. Sometimes he just reminds you of that guy at the con who won't stop talking to you about how he's planning on building a working transporter.
And in the end, the message that really comes out of it all is that as long as your heart is in the right place, as long as it inspires you to be a better person, it doesn't really matter if it's real or not. If it works for you, and in turn helps you be just a little bit nicer to your fellow man, that's what counts. The parallels to religion are obvious, if not overtly touched on; we see the New Earth Army program from two approaches, one lead by a man who wants to better the world and the people in it, and then by one who sees the potential tactical applications of psychic abilities, such as killing someone from a distance just by staring at them. For good or ill, you're going to get out of it what you put into it, be it religion, the military, your mind or your life.
In the end, it doesn't matter if it's real; what matters is what you decide to do with your belief.