Factual error: The interior shots of the Gemini and Apollo Spacecraft show worn and dirty panels, knobs, switches and circuit breakers. The movie most likely used some original cockpit trainers, but in reality the astronauts were flying brand new spacecraft that were spotless.
Continuity mistake: When the soldiers arrive at the Alamo, the soldier with the glasses is reading a book with a white cover. In the next shot, he is reading one with a red cover.
Continuity mistake: As Steve and Mike are leaving in the police car, Mike turns and puts his arm back as he looks back to start driving in reverse as Steve waves to his wife. It cuts to an angle from behind his wife as Steve puts his arm down, but then Mike turns and looks back again a second time in this shot to start backing up. (00:20:35)
Factual error: The plane used in the film to take Juliet back to London towards the end of the film is a replica of a Dakota C-47. She is painted with black and white "invasion stripes" on both the upper and lower surfaces of the wings - approved in May these were only widely put into use for D-Day in June 1944. After one month the upper surface stripes were ordered removed, and by the end of 1944 they were ordered completely removed. By 1946 when the film is set they would have been long gone from any serving aircraft still flying.
Other mistake: The Israeli commandos are painting an orange Mercedes black using brushes. In later scenes the car has perfect factory finished black paintwork.