Continuity mistake: The American flag on the raft moves from shot to shot. That can't happen, because the raft was tethered to the spaceship while Taylor was throwing the supplies down. (00:10:15)
Continuity mistake: After the ship has sunk, Taylor, Landon and Dodge make camp on some rocks. In the shot where Taylor says "Dodge, run your soil test. Got your sensors? Geiger counter?" in the background is the life raft used when they escaped the ship. The raft is resting on some rocks that are bright colored. In the next shot, in a shot of Landon the rocks the lift raft is resting on are all dark colored. The raft has also moved closer to the water. (00:12:35)
Continuity mistake: When Taylor and Landon discuss Stewart's death on the rocks, their hair goes from being blown in the wind to resting still between shots. (00:13:00)
Visible crew/equipment: When the astronauts are running down a dusty hill in the desert, you can spot the shadow of the camera on the back of Landon and Dodge. (00:15:50)
Continuity mistake: When the three are doing water check, the wide angles show Landon sitting in the sun, but the closer angles show Landon sitting in the shade. (00:17:15)
Continuity mistake: When Taylor, Landon and Dodge do water check, during the shot where Landon says "Thunder and lightning, no rain", Landon is looking down on the ground. In the next shot, as Landon finishes the line with "If we could just get a fix", he is suddenly looking upwards. (00:17:35)
Other mistake: After running from the falling boulder in the forbidden zone, Dodge walks ahead of Taylor and Landon. In one shot, Dodge is shown in the distance, but you can two tracks in the dirt between him and the others. (00:19:50)
Continuity mistake: Taylor, Landon and Dodge go for a dip in the river and they get wet. The humans then take their stuff, so they get out of the river and they are all mostly dry (still a bit damp, but less dry than they were before). (00:25:40 - 00:27:25)
Revealing mistake: In the scene where Taylor is running after the humans when their clothes are stolen, they're supposedly naked. As Taylor is running through the trees, you can see he is wearing flesh coloured shorts. (00:28:45)
Continuity mistake: When Taylor, Landon and Dodge discover the humans, when Dodge says "Blessed are the vegetarians", both Taylor and Dodge are standing even with each other and Landon is standing about an inch or two behind Taylor and Dodge. In the next shot, Landon and Dodge are standing even with each other and Taylor is standing almost a foot away from Landon and Dodge. (00:29:00)
Continuity mistake: After Dodge is killed, Taylor finds him in the field and holds him. Dodge's head changes position between shots. (00:32:40)
Continuity mistake: When Julius starts hitting Taylor in his cell, Taylor drops the notepad and pen he is holding and it lands about 4-5 inches away from him. A couple of shots later, the notepad is suddenly an inch away from Taylor without being touched. (00:45:10)
Continuity mistake: When Zira looks at the "My name is Taylor" on the notepad she says "Get me a collar and leash." The shot then cuts to Taylor in the cell. In this shot, he has a few strands of hay along his arm, but in the reverse angle, there's hardly any hay on along his arm at all. (00:45:35)
Visible crew/equipment: Right before Taylor gives the female ape (Zira) the piece of paper with his name on it, while he is fighting the other ape, the shadow of the camera is seen on the bottom of the cage. (00:47:05)
Continuity mistake: When Taylor is trying to describe where he came from to Zira and Cornelius, he has Cornelius hold up a map. Cornelius holds the left side and Taylor holds up the right. As Zira says "You fell into the water here?", the map is slanted to the side. In the next shot, Taylor suddenly isn't holding the right side of the map and the map is more levelled out. (00:48:20)
Visible crew/equipment: After Taylor flees the market, he enters a museum and begins to run down a spiral staircase. As he reaches the bottom of the staircase, to the right of shot, a cameraman's shadow is visible on one of the carvings and the staircase's support column. (00:55:30)
Visible crew/equipment: After Taylor exits the museum he is whipped by an ape on a horse. Taylor/Charlton Heston is replaced by a noticeable stunt. (00:58:57)
Revealing mistake: As Lucius tackles the guard and yells "Grab him!" to Taylor, Lucius then strikes the guard over the head, knocking him unconscious. When Lucius begins pushing the guard over to Taylor's cell, you can see the guard is already unconscious before he gets struck. (01:18:45)
Continuity mistake: When Julius arrives to escape Taylor from his cell, he gives the guard a note who has a cigar in his mouth. When Julius tackles the guard, the size of the cigar differs between shots. (01:18:50)
Continuity mistake: After Lucius knocks out the guard, Lucius then ties the guard to the cell bars. In the shot where Lucius says "I'm Doctor Zira's nephew. This abduction was her idea", it can be noticed the fingers on the guard's right hand are resting freely. Then as Taylor says "Get me out of this", the fingers on the guard's right hand are almost clenched together. (01:19:00)
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