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.
Character mistake: Mike and Steve try to get Kenny out of their squad car while under fire. The driver side of the car is fully protected as it's the passenger side that the merc is shooting at. Mike tries to open the back door on the driver side but says it's stuff and asks Steve to get Kenny out on his side... where the merc is shooting. Kenny crawls to the front of the car, they open up the passenger door and Steve pulls him out. Mike then asks if they can get Kenny around to his side. Only while he's asking this you can see the front door on Mike's side is wide open. Kenny could easily have just gotten out that way and out of the line of fire. He even crawled to the front seats but got out on Steve's side instead of the open door on Mike's side where it was safe. (00:46:30)
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.