The notepaper which is given to the Deputy Press Secretary has been torn from a pad and we see the rough edges, but a subsequent close-up shows it cut cleanly.
During the trip to George Washington Hospital, Special Agent Cage's radio hand-mic changes colors from tan to black. Also it changes hands when in fact the mic is fixed in place under his clothing.
The movie erroneously mentions Hinckley's arrest in Nashville in the previous year, Reagan was there campaigning with a cabinet member mentioning that Hinkley was very close to the president. The actual potential victim was president Jimmy Carter.
When Special Agent Cage is inspecting Reagan during the high-speed drive in limousine for wounds, the view through the windows shows protective tarping, giving away the fact the vehicle isn't actually moving.
The presidential airplane was a version of the Boeing 707 at the time of the assassination, not the Boeing 747 currently in use.
A film truck is seen on the exterior of the president's limousine during the trip to George Washington Hospital.
Orange blocking tape on the floor in the restroom where John Hinckley Jr. is confronted by the police officer. Also in the same scene, legs of a lighting stand is visible under a door of one of the bathroom stalls.
At the start of the scene where General Yates gives his "out of the box" theory.
Most of the actors bear no resemblance to the figures they are playing.