As some people haven't seen it yet, I'm putting my response in a spoler tag. It most definitely had paradoxical elements. If young Joe killed himself in the past, how did old Joe even exist to be sent back to the past.

That's why Willis disappeared back to the future style. Once you understand the rules it makes sense. It's like you can go back and alter what timeline you are on but the future of that timeline exists simultaneously with the present of the that timeline.

So Willis goes back and is worried that his memories will change, ie that he would shift to an alternate timeline but ends up disappearing because once Levitt kills himself Willis ceases to exist on that time line.

In any case I loved how they dismissed the whole trying to figure it out with the "we'll be here all day" scene. That's what I liked about the movie, the time travel wasn't really the point of the movie. It's was about one mans conflict with himself and the time travel was just there to facilitate that idea.

I think the most hand-wavy part was when they were dismembering Paul Dano and having it effect the guy who I thought was William Katt (Old man Paul Dano). Unless they were trying to show that modifications to the young one when both are in the same "time" only affect the old one at the same "that time" and not over the entire course of their life.

The Rainmaker payoff was awesome, and the kid did a great job. When I saw that scene I immediately thought "so this is what happens when Akira meets Back to the Future."

after the first time young joe tried to kill old joe and willis jumped him and escaped it cut to the montage of that scene from willis' view where he closes his loop and goes on to grow old and then travel back in time. So already you have alternate universes, one with willis getting killed and another where he escapes.

I guess the problem is that when he dies we are now in back to the future time travel where you are in one timeline and the time line forces consistency on the whole time line, ie once you die every instance of yourself vanishes.

I dont think either of those is paradoxical in themselves and are both classic ways science fiction has tried to deal with the paradox of time travel. The problem is that the writer chose one system of time travel when he needed an alternate universe and he chose another when he needed characters to die. Its just bad writing, which I guess I didnt notice because everything else was so well written. Its not really explained why when Levitt's character kills himself Willis cant just go on in a new time line other than the fact that the writer needed an impactful ending.