Revealing mistake: After Taylor gets up from being dragged in the square, another ape tries to rope him. As this occurs, the stuntman is easily distinguished.
Other mistake: As the Apes first appear on horseback, as the second one from the camera's left turns around, you can see that the rifle doesn't have an ammo clip in it.
Other mistake: After the rocket hits the water, the view of the landscape bobs up and down. But the movement at the top and bottom of the view are slightly jerky rather than the smooth stop and go that a real bobbing craft would have.
Revealing mistake: During the desert walk you can see footprints in the sand from previous takes, also dark lines in front of them which they follow like a pathway.
Continuity mistake: After the apes have blown up the cave, Taylor and Nova are shown riding away on a horse. In a close-up, Taylor looks at Nova and places his hand on Nova's cheek, but in the reverse angle he suddenly doesn't have his hand on her cheek and he is now looking straight forward. (01:44:30)
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)
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)
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)
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.
Character mistake: A space traveler would not be "going to Orion." The major stars in Orion vary in distance from the earth from 243 to 1,360 light years. Orion is only a constellation as visible from Earth; once you get away that far, the stars would not be in the same alignment as they are from Earth. They would have been going to a specific star, probably Bellatrix at 243 light years, as Taylor mentions being at 320 light years.
Suggested correction: I'm not sure what scene you're referring to, but I never heard anyone say they went to Orion. Taylor says they're on a "planet in orbit around a star in the constellation of Orion. That could be Bellatrix." To Taylor, who is from Earth, the star is still in the constellation of Orion.
I agree with your take, but I still think it could be interpreted as Orion's stars all being in close proximity. And I would hope they would know about the 320 - 243 light year issue.
Continuity mistake: When Lucius releases Taylor from his cell after knocking out Julius' the guard, his hands are shown to be tied above the horizontal lining along the cell. Then as Lucius says "We've got to move fast", the guard's hands are now tied below the horizontal lining along the cell. (01:19:05)
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)
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)
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)
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)
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)
