When Willis is in jail talking to the investigator, Aldrich, Aldrich leans over to whisper something to him. In the first shot, taken from behind Willis, Aldrich is speaking into Willis's right ear. The scene immediately cuts to a different angle, taken from behind Aldrich, and Aldrich is now speaking into Willis's left ear.
Ethan Hawke's character is seen shooting a road-side sign for target practice. The sign reads "Bandera 12M Kerrville 2M". Those two cities are roughly 28 miles apart and there is no point on the map that can be 12 miles from one and only 2 miles from the other.
The end credits feature footage from the real Joe Newton's appearance on James Coco/Joe Newton/Chet Atkins (1980). On-screen text incorrectly identifies the date of this appearance as January 20, 1980, when the correct date was actually November 20, 1980.
Brentwood and Joe watch Erich von Stroheim's Greed (1924), in Canada, during what appears to be summer. Greed was not released until December of that year, and didn't see any wide release until late January of 1925. It's also doubtful that it would have made it to Canada any time before then.
When the mail train uses its emergency brakes, sparks fly from the wheels. In the close up the pyrotechnics and wiring are clearly visible through the big wheel.
After the armoured car robbery, when the boys stop the car and fight about why it had gone so badly, a modern day wheelchair-access drop-down curb is seen. During the 20s, no such curb would have existed. They would have been straight across.