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.
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.