When Caesar scans the camp with the binoculars, Luca asks in sign language if he's spotted the Colonel. Caesar responds despite the fact that he is looking through binoculars and couldn't have seen Luca signing.
The poop on the guard's face disappears between shots.
The soldiers are standing in the rain at the border camp, yet none of them is wet.
Caesar's birthmark is different from the previous movies.
The Colonel eats a piece of fruit off the tip of his knife. He takes a small bite, leaving the rest on the tip of his knife as he goes into an intense dialogue with Caesar. The camera cuts away. When it cuts back, the fruit is gone, and there's no fruit on the floor when the camera pans out.
Luca rides a horse in much of the film, often at a gallop. An adult gorilla weighs 300-400 lbs. (136-181 kg.). A horse carrying that much weight wouldn't be able to walk easily, let alone gallop.
Chimpanzees cannot produce tears. Caesar's tears may be another morphological change granted by the drugs and the virus.
At 1:20, in the opening prologue text, the word "RISE" fades from white to red, and then fades out. In the last few frames as the red "E" is fading in transparency, it quickly jumps from red to white.
At 57:57 into the movie. After the little girl places the flower on the head of the dying gorilla you can hear somebody sneezing.
When Caesar bring his horse to stop in the snow, someone off-camera says "woo horse."