Revealing mistake: The man from Mars is in an elevator with a woman when the power goes out. He tells her he cut the electricity and gas powered engines all over the world for a half an hour. They proceed to show clips of the power out in different parts of the world. When they get to Big Ben in London, you can see a motorboat cruising down the river in the background. If the boat were powered by wood or coal, there would be plume of smoke trailing it. If it were powered by oil (ie. diesel) electricity is required to pump the fuel into the ejectors.
Factual error: In the very beginning of the movie broadcasters around the world are commenting on the mysterious spaceship. To lend a bit of calm and normalcy one broadcaster notes that despite what is happening many people are enjoying the fine spring weather in the Capital, to this end picnics and the wonderful cherry blossoms are plainly depicted. Shortly afterward when Klatu leaves the hospital, he is seen examining the cleaner's tag on the suit he "borrowed". This is where he adopted the name Carpenter. Clearly printed at the top of this tag is the date 7/18 1951, not spring by at least a few months.
Plot hole: Klaatu is shot and his body is lying in a prison cell. Gort leaves the flying saucer and walks all the way to the heavily guarded police station in downtown Washington DC. Gort is 8 feet tall and is a robot plus he uses his noisy death ray to create a hole in the police station to retrieve Klaatu's body and nobody noticed him? On top of that, he walks all the way back to the saucer unseen with a dead body.
Continuity mistake: During the news broadcast, the TV announcer is evenly lit. You can see this in the side view of him, as well as on the TV monitor that's next to him. Then, just after he says "there is no reasonable cause for alarm," the microphone in front of him is suddenly casting a big shadow on him.
Revealing mistake: When the spaceship is going to take-off, every scientists are trying to escape, but there's a man wearing a light colored suit and hat who seems more interested in pushing the chairs everywhere than escaping. He even pushes a chair in another row. The director obviously told the actors to push some chairs to create more excitement in the scene, but he seems to take that too seriously.
Continuity mistake: Just after Klaatu gets shot, Gort is seen melting the clear glass/plastic/cement material he was encapsulated in. When Patricia Neal begins to approach the space ship, the camera shows Gort still melting the material with it almost down to his ankles by this time. The next shot shows Ms. Neal looking at him, but when the camera goes back to Gort, the cement he was encased in is suddenly back up around his waist. How did it get back up when moments before it was down around his ankles?
Other mistake: As the UFO approaches and flies over the park, the camera pans to the right with the UFO in the upper left corner of the shot, tracking it. As it does, the UFO passes over the heads of two women, who are gazing at a spot behind where the UFO is when they should be turning their heads to the right, watching the descent.
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Plot hole: In the scene at Arlington cemetery, Klaatu asks Bobby if it costs money to go to the movies. Bobby states he has $2 his mother gave him, which Klaatu trades for two diamonds. That being said, how in the world did they get from NW DC to Arlington in Virginia, and then on to the Lincoln Memorial at the Mall in DC? Much too far to walk, and Bobby made no mention of money he had before to take a bus or cab.
Factual error: When Bobby and Klaatu are leaving the Lincoln Memorial, Klaatu asks Bobby where Professor Barnhardt lives. Bobby responds, "near where my Mom works, at the Department of Commerce." There is no residential neighborhood as depicted as the location of Barnhardt's house anywhere near the Department of Commerce.
Continuity mistake: After the power comes back on, a newspaper front page has Klaatu pictured with the president standing just outside the entrance to the saucer's dome, and Gort standing about five feet in front of Klaatu in the same place. But early in the film, Klaatu was on the ground with the president, and Gort never preceded Klaatu coming out of the saucer.