I thought the movie was above average. I really liked the characters and the universe created, and would have rated the movie excellent, except the second half was a little slow and the time travel mechanics don't make sense (but I have accepted that element).
(Apparently in the script the scene in the diner actually has them explain time travel with straws but in the movie they just had Old Joe (Willis) ridicule that concept. If anyone actually has the script, I would be interested in reading that scene.)
Anyway, to address the two main points I would like to clarify for people:
1. The basic premise is that murder at some point in the future is too difficult to get away with, so future mobsters send bodies back to be disposed of. You must accept that premise as the background and move forward from there. Critiquing the movie on that point is like critiquing the movie for having time travel at all saying that "time travel inherently makes no sense." Slightly more valid question is why they don't send their victims into the distant past, but again, the premise is the premise; I don't think the details of the "tagging", etc. need to be explored when the focus of the movie is on identity, selfishness, violence, impact on children, etc.
2. Despite still not liking how the mechanics of time travel were depicted (the fact that injuries to the younger versions affect the older versions of people, but nothing seems to affect all the events leading up to that moment makes no sense in any logic), I have come to appreciate the movie slightly more than I did upon leaving the theater. I don't like it, but that is how the time travel works in this movie. The good thing that it does is that it allows for a kind of hybrid time travel mechanic where paradoxes are allowed and not allowed at the same time. In this case, the biggest outcome is that Joe can influence Cid and Cid's mom's lives (preventing Cid from becoming the Rainmaker) and still having his personal journey and duel with his older self.
Right up until Young Joe made the decision to shoot himself I was thinking that the movie would have Old Joe "realize/remember" the revelation his younger self came to, and would put down the gun. In fact, all through the movie when Old Joe was fighting to remember his wife in the face of his shifting memories, I figured that Young Joe's character development would shift Old Joe's character around until they were closer to being the same person. Where at least they would see the big picture in the same way and no longer be enemies, but that is simply not the way the movie went.
Now a thought that later baked my noodle was wondering why the mobsters would still have guns in the future? Especially when going to kidnap a former looper. That looper obviously knows you don't want to use the gun, the whole reason you are kidnapping him is to avoid killing him in that present. So it makes no sense to have it, especially when they have perfectly effective "stun guns" in the same scene. That was obviously a plot point made simply because it had to be and the director didn't think through the logic of it. JGL even alludes to it when he discusses the shotgun at the farm; he isn't afraid of the gun because he isn't afraid of the person wielding it. Old Joe would never be afraid of any mob employee carrying a gun in the future.