I watched Looper yesterday and was quite impressed.
There are six interesting characters in the movie which act as crucial elements in effecting the alterations in timeline versions.
Baby Cid, Rainmaker Cid, Young Joe, Old Joe, Old Joe's love-Chinese lady and Sara
The original timeline is the most intact version which gets neglected because of how short it was shown in the movie. Eventually after 30 years, the Rainmaker, a genius TK mutant sends looper's future self back to the past closing the loop. Young Joe kills his old self making the Rainmaker successful. This would continue in every version until one character, the Chinese lady love in Old Joe's timeline goes responsible for an alternate version. The premise of the following events in this version shown during the first and third time in the movie is where the rest of the film picks up to the audience’s thrill.
The Chinese lady's kiss comes as Old Joe's savior (evident from the diner scene conversation) which induces a higher reflex in him to out power the Gat Men/mob hire and use the time travel himself to make young Joe miss him as seen in the second/alternate timeline version of the movie.
Old Joe’s existence is for a single purpose. He needs to get back to the past for hunting down baby Rainmaker (reminds me of Terminator) to erase him from his timeline and thus save his love.
Baby Cid is Young Joe's savior from Gat Men. He uses his telekinetic powers to kill. This is an important event in the alternate version of young Joe's timeline. He inadvertently develops affection to the child. He falls for Sara and her devoted parenting. This is also why he decides to kill himself and in doing so he would erase the vicious infinite loop responsible for the Rainmaker's birth.
Sara tries to save baby Cid from Old Joe's gun point. She dies in the attempt during every version where Old Joe gets back to the past safe, UNLESS Young Joe decides to take his own life. By this, he has not only erased Old Joe but also the Rainmaker- TK Hitler of 2074 from his version of timeline.
I would say this ending IMO has worked well for the movie's success. The penultimate scene shows baby Cid (reminds me of young James Cole of “The twelve monkeys”) and makes us assume he gets a better life with Sara since then with the alteration of events. Yes of course, no denying that there are paradoxes created by examining various sequences in the movie. Apparently the movie scores like every other time-travel movie with an original content. My previous favorites having time-travel elements from the Multi-verse system with very less paradoxes were ‘The twelve monkeys’ and ‘Donnie Darko’. Both seemed equally brilliant.
