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)
Factual error: The film is set in the 1930s, but when there is a closeup of a sheet of text (a conversation between Billie and John), it is typed out in a computer font (which did not exist) as opposed to a typewriter.
Factual error: When Special Agent Winstead is leaning over Dillinger to hear what his last words are, you can see that he's wearing modern-day contact lenses, in 1934.
Factual error: During the movie Dillinger talks with Baby-Face Nelson about a train job. The train is visible in the background. The train however is the Union Pacific locomotive 844. This locomotive was not built and delivered to the Union Pacific until December 1944, 10 years after Dillinger was killed.