Revealing mistake: When McDonald is in the tunnels and is called to pick up the phone, he picks up a red phone. It is a standard Bell TouchTone desk phone. To make the phone look more futuristic, there was no cord and it was disguised as a cordless phone. The port that the cord would plug into is covered by a piece of colored tape. This also can be seen in the operations center of Ape Control when the worker picks up the phone.
Continuity mistake: When the apes are breaking into the command post, just as Breck says "Shoot them! Shoot them all!", the door is about half sliced down. A few shots later, the door is almost entirely sliced down with no time to do so. (01:13:25)
Continuity mistake: After the apes began revolting in the communication center, Governor Breck shoots an ape in the face. Blood splatters on the uniform of the officer holding the ape. A moment later the officer stands up, but his uniform is clean. This is the unrated version. (01:36:30)
Revealing mistake: In the electrocution scene, whenever Caesar is screaming you can see the hole in the roof of his mouth for Roddy to breath through the front of the makeup.
Revealing mistake: During Caesar's big speech at the end, you can tell in some of the close-ups of his face that his mouth isn't moving.
Other mistake: In a scene after Caesar picks his name where they are outside then walking down stairs outside the civic center in the plaza (filmed at UC Irvine), you can catch a quick glimpse of students or faculty in the upper right corner with cameras taking pictures.
Other mistake: We know that, after Cornelius and Zira were executed at the end of the previous movie, "Escape from the Planet of the Apes," baby Caesar was only an infant who was just starting to say "Mama." In "Conquest," we know that 20-year-old Caesar was raised (and secretly educated) by Armando, the circus owner. But, after 20 years of being raised and secretly educated by Armando (who has a thick Mexican accent), Caesar has a distinct British accent.
Chosen answer: Caesar wasn't the only surviving ape, just the only surviving talking ape. Conquest of the Planet of the Apes is set roughly 20 years after Escape from the Planet of the Apes, and in that time man began to keep apes as pets (disease wiped out dogs and cats) and (most likely through breeding), the apes evolved into what we see in the film.
Bishop73