Continuity mistake: When the hero and his group comes out of the ship wreck and you get a shot from some distance back at the ship, look to the far right and you will see a road (sloping down towards the ship) with clear tire tracks on it. Whose car might that be?
Continuity mistake: When Leo and his group of rebel apes are starting to ride their horses across the river, Helena Bonham Carter falls off her horse and he swims across the river with her on his back. The other apes can't follow because they're afraid of water. So they arrive horseless. However, when they get across the river, suddenly everybody has horses.
Continuity mistake: When all the humans are about to be branded, one of the humans is removed from the cage and the funny old ape just pushes the cage door shut, not locking it. A few moments later the camera pans round and you see that the cage is now bolted.
Continuity mistake: When Leo dives in the pond where his pod crashed, to get his bag, it is dark and dingy, yet when you see an underwater shot the water is a clear blue/green colour and you can see the sun (or some form of light) shining through the water, yet when he comes out there is no light and it is dingy again.
Continuity mistake: When Leo gets into the pod to try to catch the chimp's pod, he puts on his helmet. Look away, look back, and he's all snapped and buckled in, which would have taken several minutes at least.