Revealing mistake: When McDonald is in the tunnels and is called to pick up the phone, he picks up a red phone. It is a standard Bell TouchTone desk phone. To make the phone look more futuristic, there was no cord and it was disguised as a cordless phone. The port that the cord would plug into is covered by a piece of colored tape. This also can be seen in the operations center of Ape Control when the worker picks up the phone.
Revealing mistake: Freeman Lowell has several cargo containers dumped off the spaceship, to make it appear the ship has suffered an accident. A wide shot shows the ship receding in the distance, with the containers rolling weightlessly in the foreground. As the foreground containers pass slightly in front of the more distant ones, they don't mask them; their images overlap. The containers were apparently composited into the shot with simple multiple exposures. (00:35:40)
Revealing mistake: When Stewart's wrestling with the alligator look closely and you can see the black strap keeping its jaw shut.
Revealing mistake: The protagonist jumps from a bridge and boards the train to try to save the Professor. When he is walking on the top of the carriages, look at the treetops in the background; the train is stationary. (00:12:00)