After testing the release of the wire net from the helicopter, an enlisted man with one stripe on his uniform says to Col. Calder, "The hook's working fine, sir!", to which Calder replies, "That's good, sergeant!" One stripe is the insignia of a private, not a sergeant.
The General, fearing that the space ship has sunk, points to a body of water on the map and says that the lost astronauts are now "20,000 leagues under the sea." Of course, it's a coy reference to the recent sci-fi flick 20000 Leagues Under the Sea (and Jules Verne's novel). However, a league is about 3 miles; no ship could sink 60,000 miles under the sea since the earth isn't that large. The Verne title refers to the amount of miles traveled under the sea, not how deep the craft was operating. So the General has made a geographical error while trying to make a hip quip.
Near the beginning when the spaceship starts to sink, the meteor hole starts to go under water. The next shot is from the inside and the hole is still above the waterline. The next shot is outside and the hole is almost covered with water.
During the fight in the barn the stain on the Colonel's bandage grows from a small spot to two long streaks and then to a large stain covering most of the bandage. But when Marisa Leonardo asks to change the bandage the stain has shrunk to about half the size.
In the sequence where the large military helicopter is searching for the Ymir, there is an aerial shot taken from above the helicopter as it skims over the fields. The helicopter casts a big shadow as it flies, and if you look directly in back of that shadow you can see a smaller shadow trailing it, which is that of a smaller helicopter that is filming the scene.
It is stated that the craft was spotted by radar over Iceland at an altitude of 200, descending at 3,500 feet per minute. It was then tracked again later, still descending at 3,500 feet per minute, and they project the landing position. However, at that rate of descent, it would take 5 hours to fall 200 miles. During that time it would make over 3 orbits of the Earth, so it would not be possible to simply look at a map and point to a landing location.
William Hopper's character, an Air Force Colonel (note clouds and lightning bolts on hat brim) would be wearing a navy blue hat with his tan uniform, not an olive drab Army hat. Also, General's stars and Colonel's eagles would be silver, not gold. (Colorized 50th Anniversary version).
The rate of descent by the space craft that is talked about at the beginning of the film is 3500 feet per minute. That is less then 60 mph. No object reentering the atmosphere from "space" could move so slow. Reentry speeds are measured in the thousands of miles per hour.
During the fight between the Ymir and the elephant, there is a tight shot of three men hiding behind a pillar of the viaduct. When the two animals get close, the turn and flee, one of them falling backwards, and another tripping over him. In a wider shot scene a few seconds later we see the same pillar, the same men run up to it, hide and watch the fight as before then turn and run, as before, tripping over each other. It's then same shot used two times closer/farther perspectives.