Zira's first line in the presence of humans, "Because I loathe bananas!", is a reference to Kim Hunter's real distaste for this fruit, which originated during the filming of the first Planet of the Apes (1968). The actors portraying apes were required to keep their makeup on during breaks in order to save time, so the rest of the crew often called them monkeys and offered bananas to mock them.
The trivia items below may give away important plot points.
Sal Mineo found the make-up uncomfortable, so the script was re-written to kill his character off earlier than planned. This was Mineo's final theatrical film before he was murdered on February 12, 1976 at the age of 37.
For the death scene, Cornelius and Zira were originally going to be ripped apart by a pack of Doberman Pinchers (the feared dog from that decade) by Doctor Hasslein. But producers thought the scene would be far too gruesome so they were killed by gunshots instead.