Continuity mistake: At the Dam Hydro Plant Caesar throws Koba on his back and pummels him. Then they roll once to the right, which now puts Koba on top of Caesar. Yet a quick-cut to their faces shows they kept Caesar on top, still pummeling Koba.
Suggested correction: It's Koba on top of Caesar in the first part of the fight. Caesar gets the advantage after the roll to the right.
Continuity mistake: When Koba is approaching the soldiers to kill them, he is smiling and jumping around, then he makes a front flip, but the distance between Koba and them changes between shots.
Continuity mistake: The Apes cross the timber-pile beaver dam en route to the hydro-station. On their approach, the upstream canyon is shown to have a low water level. As they cross, the water is spilling through that dam.
Suggested correction: Water is flowing away from the dam, so that is the exit side and the level would be dictated by the flow through and over the dam.