When Dr. von Essen is directing the monster Lt. Prescott over the PA system at headquarters, he tells him to "turn right" - whereupon the monster-Prescott immediately turns left.
When Commander Prescott exits a building, he passes a sign that reads, "Flight Operations - Authorised Personnel Only". The film is set on an American Air Force base in New Mexico, and no sign in the United States would use the British spelling of "authorized", with an "s" instead of a "z". (The fact that the film was shot in England accounts for this error.)
At 19 minutes into the movie Dan Prescott is looking out the window at a rocket that's just lifted off. The rocket is at least hundreds if not thousands of feet in altitude when Prescott says 'look at that thing go'. However, Prescott is looking down out of the window when the rocket would clearly have been high in the sky. In fact the window blinds in the window are positioned in such a way that Prescott wouldn't have been able to see the rocket in the air, anyway.
Controllability barrier incorrectly regarded as an error. this did not exist, per se, but a single rocket propelled craft with no attitude thrusters could reach an altitude where the air is so thin that aerodynamic control surfaces would be ineffective. hence, 'controllability barrier'.
The test aircraft are repeated said to have to pass through "the heat barrier" and then "the controllability barrier" - two "barriers" that do not exist.
Wilson introduces himself as the "Assistant Chief of State Police". There is no such rank or title in American police forces; "Deputy Chief" would be the most likely title.
Though set in New Mexico, the film (except for some stock and establishment shots) was shot entirely in England, which is why scenes purportedly taking place in an arid state in the American southwest desert feature heavily forested areas with trees, hedges and shrubbery unknown in New Mexico, cold ground fog, and English-style houses and country roads.
At the end of the opening credits, the Y-12 is shown deep in outer space, yet soon after Commander Prescott states that the plane is at an altitude of 10,000 feet - less than two miles.
When the police car is chasing Dan, British style road signs are seen on the left hand side of the road clearly showing that it was filmed in the UK.
At the end of a highway chase, a police officer shoots the monster 7 times with a revolver without reloading.
In addition to the already-mentioned goof regarding one sign using the British spelling of "Authorised" instead of the American spelling (with a z instead of an s) that would be seen in New Mexico, Commander Prescott twice enters yet another building (the University of Albuquerque Aviation Medicine Dept.) with a sign reading "Scientific Station Authorised Personnel Only".