I thoroughly enjoyed the movie. It's nice to sit down watching an original film, not knowing what is going to happen next and genuinely being invested in the characters.
The only scene I didn't like was Bruce Willis doing the movie hero shoot 'em up scene. It simply belonged in another movie, not this one, and was a bit silly.
Everything else, though? Pretty good.
The bit where the other guy's loop had his limbs suddenly vanish didn't really make much sense, but its part of the internal logic of this film's universe, and they kept it consistent. I actually reminded me of the photo in Back to the Future.
I figured that Emily Blunt's character had been a hooker/junkie like Piper Perabo's character and had become aware of Looper's that way.
It doesn't really make sense to send them back in time to be killed and then disposed of. I think it would be easier to kill them then send the body back; maybe even gas them in the time machine before sending them. But maybe its like the Terminator.
It's also a bad idea to have Looper's kill themselves; better to send them to another Looper who won't care.
Killing the Looper's while their young won't work. They sign up enough money to retire in their 20's and live the high life for 30 years. If they know they won't live to spend that money then no one signs up.