Early in the movie, Dr. Martin crashes his Studebaker coupe into a tree. Later, when he is going to the power station, the Studebaker is undamaged.
When Dr. Kruger leaves his office, he is clearly seen turning off its lights. A few minutes later, Dr. Martin opens Kruger's office door, and from the outside the office is still dark. But as soon as Martin enters and the scene switches to the inside of the office, the room is suddenly light again, though he hasn't switched on any light. (Dr. Martin turns on a light switch after entering the already-lit office, but this switch appears to be for the room containing the safe, and in any case no light comes on in the office itself when he does turn this switch on.)
During the chase through the powerhouse, Dr. Martin passes a wall of instruments where he pauses briefly in front of a clock reading 10:43. A few moments after, the group chasing him also stops briefly before that very same clock, showing the same time. But less than a minute later, in the control room, the clock on the wall there reads exactly 10:00.
When the rescue helicopter is seen it changes from a Sikorsky H19 Chickasaw to a Bell 48 H-12 even though the plot suggests there is just one helicopter.
When Briggs is on the phone with Banks there is a chair in front of the flag but in the next scene when Mrs. Martin is sitting on the couch there is a stand with a vase of flowers in front of the flag.
When the alien scientist is showing Dr. Martin their energy storage system, he says they've stored "several trillion electron volts (eV)" of energy. While an eV is a unit of energy, it is a very small one. One trillion eV would be enough energy to power a 100 Watt lightbulb for slightly over one million-millionth of a second (1.6 pSec to be more precise). Dr. Martin (as a nuclear scientist) would have known this was a small amount of energy, so it can't be put off as the alien misusing unfamiliar terms.
The radio in the gas station is receiving police calls, but is it simply a Crosley AM radio. Police call frequencies are far beyond the range of a standard AM radio.
The approaching shot of Astron Delta is through a layer of clouds..in space.
The nuclear explosion at the end of the film is stock footage of an atom bomb test conducted in the Pacific a few years earlier (which turns up in many science fiction movies of the 50s), and you can clearly see the ocean and the fleet of ships blown up as part of the test through the window overlooking what is supposed to be the Nevada desert.
The last name of actor Frank Gerstle (who plays Dr. Kruger) is misspelled in the end credits as "Gerstel".
In most of the shots of Dr. Martin's plane circling in the air and as it plummets toward the ground, clouds can clearly be seen through the aircraft.
In the shots showing the supposed "fireball" on the ground, a couple of vehicles can plainly be seen on the highway to the right. (Since the shot is a freeze-frame effect, the vehicles are motionless but still evident.) Also, since this is a nuclear test site, there shouldn't be any highways, let alone traffic, in the vicinity to begin with.
The microphone used to record Dr. Martin's confession is a desktop shortwave radio pushbutton microphone. When the button is up, it acts as a speaker. You have to depress the "talk" button on the base in order to transmit. The FBI agent just holds the neck of the mike stand without depressing the "talk" button. This type of microphone was incompatible with tape recorders then in use in the 1950s.
After the FBI agent regains consciousness on the ground, you can see the piece of paper, containing top-secret information that Dr. Martin was supposed to leave under the rock, next to the FBI agent. When the FBI agent gets up he leaves the piece of paper on the ground, goes to his car, answers the radio, and then leaves without going back to get the piece of paper.
In a top secret installation none of the offices are locked, Krueger leaves his window wide open and there is no gate at the main gate.
Denab shuts the cage door behind Martin to trap him in with the huge animals they are breeding, then later opens the cage to let Martin back in, asking him, "Don't you think you would feel more at ease on this side of the cage?" But both before he shuts Martin out, and after he lets him back in, the cage door is wide open - leaving the Astron-Deltans themselves at risk of being attacked by their giant insects and animals.