Factual error: In one scene, focused on a period wood-staked pickup truck parked on the street, you can see clearly a modern Jeep Grand Cherokee parked on the other side of the street.
Continuity mistake: When Dillinger is looking at his watch just before going to the movies, the time is 6:02. Close-up of his mum's photo, and the time is now something like 6:25.
Factual error: Early in the movie, during a bank robbery, there is an FDIC sign beside the teller. Dillinger's bank robberies were mostly in 1933, he was arrested in January 1934. The FDIC was not enacted until January 1934, making it impossible for the bank to have been insured by the FDIC during the 1933 robberies. Additionally, in the same robbery, the teller displays $5 bills that are the current format (multiple colors, offset picture, larger numbers) which would not have been present at that time. (00:42:40)
Chosen answer: Baby Face Nelson doesn't pick up Dillinger. He picks up the characters played by Stephen Dorf and another associate. Dillinger and Hamilton escape through the woods and steal a car from an older man they come across in the forest. After the shootout, Dillinger and Nelson are never in the car together.