1.   The central conceit of the film –– that injuries/death of the "present day" version of a person (lets call him "Mr. X.) will somehow flow through time, loop back, and manifest themselves by impacting the older version of "Mr. X" from the future who has traveled back in time to the "present day"  is just really really BAD sci-fi.    The reason is that both the temporal incursion from the future, and then the DRASTIC changes to a person central to this part of the time line serve to "sever" the original time line and create a new branch that proceeds parallel but separate to the original.   Even if it didn't violate all the rules of time travel that philosophers / scientists have postulated, its just dumb "as applied."  Take the guy whose fingers, legs, tongue, etc., were cut out.   To believe that his injuries translated back through a loop to his future self, you have to believe that (a) he survives his mutilation; and (b) that the bad guys contain TOTAL control of him for the next 30 years ... otherwise he could hide, commit suicide, turn in the bad guys in the future, or otherwise do something else in the future and never come back in time in the first place.   The flaw in this conceit also applies to the notion of memories traveling forward and looping back to the future self of a character.  The climax of the film, or the need for the climax on this, is destroyed by this problem if you think about it.  Despite this overarching flaw, lets just leave it "as is" and critique the rest.

2.   We're supposed to care about and cheer for a protagonist who is an unquestioning murder/killer junkie.   Seriously?   That's all they could think of to wrap around their core story mechanics?  A hitman whose role and contribution is so rote that it could have been done by a machine?

3.   And lets talk about that...  the mob controls time travel and all they can come up with is using it as a means to create a simply kill and dispose scenario for hits?   Really?   So why don't they just kill the target with a shot to the head before putting him in the time machine?  And what about people whose bodies they need to get rid of but who die right there in the future.   If burning the body in a fire was good enough for Bruce Willis' wife, why all the bullshit for other folks.  Also, if you have a machine that can make incursions through time and space, one thing it HAS to do is compensate for the enormous movement (at the rate of millions of MPH) of the entire solar system relative to the center of the galaxy and of the galaxy through space.  If you have that level of control, why not just send the targets back into the vacuum of space?  Or, if it has to be a terrestrial destination, why not send them to the bottom of the ocean in "pre history."  This is just such a stupid core piece of the movie that it makes the whole thing into a joke.  

4.  Of all the Hollywood tropes, I gotta say that the "junkie whore, who got her shit together and is now a badass with a heart of gold" is SO fucking played out.   Oh, and this former junkie whore can run a farm and deal with a telekinetic fiend of a kid all by herself but she's so fucking dumb as to, pretty much at random, decide that she'd like to bone a murderous junkie looper who is connected somehow with folks coming to kill her kid?  Really?   God, if I were a woman I'd be insulted that they even wrote a female character so fucking stupid.

5.  Speaking of stupid... at one particular point in the film, the former junkie whore knows (a) the looper with her is the present version of the guy who is coming to kill her son; and (b) the present looper's knowledge that her son is the "rainmaker" (under their monkey-retard time travel rules) means his future self knows not only that the kid is "the one" but everything they're doing in terms of trying to escape.  I don't know about you guys, but my sense is that's a pretty good time for former junkie whore to kill our protagonist and end the whole problem.

6.  Not nearly enough information about the rainmaker to give the audience true moral tension about the future of the little kid.   We know so little about exactly what was wrong with him in the future (beyond the fact he was killing a bunch of junkie hit men executioner scumbags) that the film-makers find themselves having to resort to computer enhanced "evil face" imaging on the kid so we know "look! he's really mean!"   Ham fisted and totally shit for writing there.

7.  The introduction of telekinesis early in the film is so fucking awkward and poorly executed that you just know its going to be "deus ex machina" later in the film.  Sure enough.....