Continuity: In the scene where Old Joe (Bruce Willis) is forced to the time machine and then fights back, the amount of Gat Men changes. 2 are seen bringing him in, another collecting the gold and the brown jacket, and a fourth opening the time machine. However, when he fights back there are only 3 bodies. It is plausible but unlikely that the fourth man would have left and gotten far enough away not to hear the fight.
Revealing: Considerable efforts were made for this film to have Joseph Gordon-Levitt resemble Bruce Willis (colored contacts, nose prosthetics) since they are playing the same character at different ages. Yet the two actors' ears remain distinctly different. Bruce Willis's ears are much larger than Joseph Gordon-Levitt's, and Joseph Gordon-Levitt has connected ear lobes while Bruce Willis does not.
Continuity: In the diner shootout scene, Joseph Gordon shoots at Bruce Willis missing and shooting the window out that's right next to the blue lighted sign on the wall. After more loopers arrive to kill Bruce Willis, Bruce shoots the same window that was already shot out in the next scene in order to jump out of it.