The astronauts find a plant which they declare their first "life" seen on the planet. They are oblivious to the grassy ridge behind them, seen when they are squatting. Scientist Dodge's first reaction to the "life" is to tear it up for no reason, something no sensible, ethical person would do.
(at around 10 mins) After Taylor jumps into the water from the sinking spacecraft, his hair is soaking wet as he comes up to the surface, yet in the very next shot, as he's swimming toward the life raft, his hair is dry.
When Taylor is stripped in the "hearing" scene, it is supposedly because his clothing stinks, in long shot he is left holding the stinking clothing up to his chest which doesn't make sense as the clothing would still stink, but in close shots he is not holding his clothing to his chest, implying that he is nude, and then when he freaks out and they hold him down he is clad in his original outfit again as if he had never been stripped.
As Taylor shaves himself on the beach in the last scenes, we can see he has cut himself in several places on the left side of his face. During his close-ups in the subsequent cave scene, there are no cuts visible.
Early in the movie during the establishing shots when the crew are marching through the desert through to the Forbidden Zone, a panoramic shot of the surrounding canyons shows a man next to an automobile in the distance.
(at around 7 mins) In the opening crash sequence water is seen flooding into the space ship under tremendous pressure. The crew compartment is the part in the air and since the ship is "floating" half in half out there would not be that kind of water pressure.
(at around 9 mins) Just before the spacecraft sinks, all the power goes out, and the crew abandon ship. Taylor takes a final look at the stopped clock, frozen in the last moment it recorded, as clocks do in real life.
The exposed skin of the actors' neck can be seen beneath the ape masks in a few scenes where the actors suddenly turn their heads. Such as when Buck is questioning the order to release Taylor and when Cornelius is arguing on the beach at the end.
At the end, Taylor discovers the wreckage of the Statue of Liberty and earlier a map Cornelius shows Taylor is obviously southern New York with Long Island to the east. But where the astronauts crash is obviously in the American southwest - too far to walk on the three day supply of food and water they have. Even in the event of an atomic war, the geography would not change around New York to mesas and plateaus.