Factual error: At the point where Jared Leto is released from prison he is picked up in a 1960 Black Chrysler Imperial. As the camera rises it shows the date as 1954. The car is used a few more times in the movie.
Continuity mistake: Nicke enters the room to execute a Yakuza after a woman cuffed both his wrists. When Nick shoots the cuffed Yakuza in the head, the cuff on the right is suddenly detached and bent out of shape.
Continuity mistake: In one scene Nick cuts off his two pinkies and a few scenes later the Yakuza guys are at the club drinking. When Nick drinks from his glass, you can see his pinky finger is back. (01:03:12)
Factual error: Almost mid-way in the movie there's a street scene in which a Vietnam era Huey helicopter flies overhead in 1954. (00:56:56)