Revealing mistake: After a shootout with Baby Face Nelson at a hotel, Melvin Purvis converses with J. Edgar Hoover over the telephone. As he says, "Our type cannot get the job done." Watch the background. You can see a modern era train move along the tracks in the darkness. This is inconsistent with the film's setting of 1933/1934.
Continuity mistake: During the scene of the fight between Dillinger, and Melvin Purvis and the Little Bohemia Lodge, it shows Purvis shooting from the side and he has a straight magazine in his Thompson, but when the shot faces him he has a drum magazine in his Thompson, but when it goes back to his side to reload, he again has the straight magazine.
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.
Revealing mistake: In an aerial shot of Lincoln Ave in Chicago outside the Biograph Theater the rubber mats laid on the road to look like 1930's brick streets only cover the middle 1/3rd of the street. On the outside 2/3s the street is modern asphalt and shows striping tape for bike lanes.
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.
Continuity mistake: When they break out of the Indiana jail they leave in the sheriff's own vehicle. The vehicle has no markings on the driver side door. When they arrive at the traffic light and the scene is panned you can see Police written on the drivers side door. Then they zoom in on the traffic light and above and to the right of the light in the window glass you can see the reflection of numerous vehicle driving by on an empty street. Then its back to the marked vehicle with an officer in the rear seat wearing a police hat. Then its back to the original unmarked vehicle as they drive away.
Other mistake: In the scene where Dillinger and his gang raid a bank and take the bank manager and a teller hostage, they come out shooting with machine guns and jump into and on the running boards of the getaway cars, all through this encounter the bank manager shows no concern for his own safety, no reaction whatsoever to flying bullets and loud gunfire, very strange.