In the train, when Roy is grifting the sailors, you can see
that he is only rolling one die at a time. However, you can distinctly hear him drop two dice (out of the frame) to the table at the end of the game.
At the end of the movie, when Lilly picks up the briefcase full of money to flee Roy's hotel room, several bills can be seen sticking out of the briefcase. However, in a previous shot, where she closed the briefcase and set it on the floor, these bills were not visible.
At the end of the movie when Lilly is leaving Roy's apartment with his money, blood is clearly visible on her knees and calves. But moments later when she is going down in the elevator, her legs are clean.
A cop takes Roy to Phoenix City Hall to identify a body; in Phoenix, as in any other major US metropolis, the city morgue is a separate site not located in same building used for transaction of municipal business.
When Roy goes to identify his mother's body, he states that his girlfriend's body is his mother's. There is no way that the coroner would say that a woman just a few years older (8 to be exact) could be his mother.