In order to make Gort's body appear seamless, two different costumes were created, one that opened in the back for front shots and one that opened in the front for rear shots. Unfortunately, as someone has already pointed out on this site, it was sometimes rather difficult to co-ordinate which suit was needed for which shot and thus there are several times in the film where Gort's seams can be seen. See more...
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Continuity: 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.
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: 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?