I watched the movie... and, to be honest, I had no idea what it was about before I started. But I'm into relativity and that sort of thing so I found it interesting.
I'll try not to give too much away but if you read on you might get some slight spoilers... so read at your own risk.
The gist of it is "Time cop" meets The NSA but less lame. And the premise is that the universe follows the "May worlds" theory: http://en.wikipedia.org/wiki/M...
The film uses Many Worlds to try and resolve the "Boot strap paradox": http://en.wikipedia.org/wiki/B... and/or the "Predestination Paradox": http://en.wikipedia.org/wiki/P...
Now, when you start watching it the movie kind of harms itself in that, it doesn't explain this at all... there are no convenient scientists around to explain possible scientific ways out of what we would generally consider not possible even in science fiction. I think it would have been helped by such a device. It wasn't until after I watched it, saw the ending, and then thought on it for a couple of days that I really understood what they were trying to get across.
***More spoilers, dont read if you don't want them!***
I think that the primary characters in the film were in a "Many worlds" universe and as such I think that the dance you see has been played out infinitely in many other versions of the universe. Furthermore what I think the film suggests is that these universes can interact and that the actors are not just traveling in time, they are also traversing these realities. So the events in the film may be in a closed loop, but that loop was started by the characters arriving from other "Worlds" etc... Perhaps this world existed all along, but the paradox they created collapsed "The past", etc...
The film does not explain this well at all, and I'd not take anyone that wasn't really into hardcore scifi to see this. I barely grasped it and I read the hardest hardcore scfi available every day. As far as film goes this is about as mind bending as it gets. The acting was good... but the device revolving around the main characters gender was very very clunky. I did not like that at all, and it was Rocky Horror picture show silly in its presentation. I'm not sure how else they could have pulled that off, but they should have tried a lot harder.