Revealing mistake: When Taylor approaches Miss Liberty, there should be horse tracks in the sand extending to the end of the frame. About 1/3 of the frame shows smooth sand preceding some horse tracks.
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.
Audio problem: After Taylor's been hit Dr. Galen says "he's lost a lot of blood", but his mouth is not moving.
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.
Revealing mistake: During the trial Honorius walks around the room and stops to deliver his words. Watch his feet and you'll notice a dark spot right where his feet are, which serves as the marker.
Continuity mistake: When Julius beats Taylor he protects himself. The position of his hand changes between shots.
Visible crew/equipment: When Zira locks Nova in Taylor's cell watch the left iron bar and you'll see the shadow of the camera approaching.
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.
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: 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.
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.
