Continuity mistake: At the end of the movie when Taylor and the woman find the ancient ruins of the Statue of Liberty, their distance from the statue seems to change between shots. In the first shot (when it only shows them and the torch) they seem to be almost next to it. In the next shot (when it only shows them and the crown) they are farther away. And in the last shot (when it shows Taylor kneeling from behind and the full torso of the statue) he is even farther away from it.
Continuity mistake: When Nova is removed from Taylor, one ape is also soaked with the hose. Then he is totally dry while taking Nova out of the cage.
Continuity mistake: Shortly after the astronauts crash land in the desert lake, they discover that the female crew mate is dead, her body is mummified due to an air leak in her cubicle. The mistake is that when her body is first seen, the arms and hands are folded across her chest. Seconds later, when the water starts rushing in, the point of view from inside her cubicle shows her arms at her sides.
Continuity mistake: When the 3 of them are swimming and one sees foot prints, he calls to Taylor - when Taylor starts out of the water his hair is wet, but when he stands up out of the water it is dry.
Continuity mistake: After Taylor dismounts the second ape, he attacks the ape, and the whip/rope used is dropped and Taylor is a few feet from it. In the closeup, he suddenly has it in hand.
Continuity mistake: Towards the end when Taylor is shaving, they show a shot of him when he is nearly finished; only a small dab of the shave cream left on his chin. Cut to a shot of Lucius and Cornelius looking at him from behind and his face is completely lathered once again.
Continuity mistake: When Taylor and Nova approach the Statue of Liberty, there is a slow panning shot looking down on them from behind the statue's crown. All of the spikes on the crown are completely straight when seen from this angle. When the camera angle changes and we're looking up at the statue, there is a spike on the left side of the crown bent outward. The bend starts a little more than half-way up the spike; it would have been visible in the shot from behind.
Continuity mistake: At the beach when Cornelius reads the scroll his fingers swap between being under the scrolls to being on top.
Continuity mistake: When Taylor discovers Stewart's corpse his hand is on his chest but a shot later it's by his side.
Continuity mistake: While during the trial Honorius says Zira and Galen experimented on Taylor his right-hand swaps between being by his side or resting on the chair.
Continuity mistake: When Julius beats Taylor he protects himself. The position of his hand changes between shots.
Continuity mistake: Zira visits the cages and asks Taylor if it still hurts. Taylor holds the iron bars with both hands parallel to each other. A shot later his right hand is positioned higher.
Continuity mistake: When the three arrive at the planet Taylor asks for water and Dodge shows his canteen. Check the strap of his backpack changing between shots.
Continuity mistake: When the movie begins Taylor starts rolling up his left sleeve with his right hand. Shot changes and his hand is away and the sleeve is already rolled. Up.
Continuity mistake: After Zaius warns Taylor not to go to the Forbidden Zone, Taylor turns the horse to face Cornelius. In the closeup after Zaius tells Taylor "You may not like what you find", he turns the horse around again.
Answer: I think that this is meant to be a mystery. Taylor/Charlton Heston, an astronaut, leaves a world set somewhat in the future after 1968 (when the movie was made) but still recognisable to cinema-goers at the time, to travel through a "time vortex" to arrive in a world in a distant future, which has changed beyond recognition. Taylor meets the orangutan Zaius/Maurice Evans, and Zaius hints that he has some idea of what had happened, but Zaius' knowledge is either limited, or else Zaius is not going to tell Taylor (or his fellow apes) the full story. At the end of the movie Taylor discovers that, at some point between his leaving his own time and arriving in the "Planet Of The Apes", the world had been devastated by a nuclear war, but I think that the exact time, causes of, and course of this nuclear war are deliberately left as a mystery. Sometimes I think a bit of unresolved mystery actually improves a story, and I think this is the case here.
Rob Halliday