During breaks in filming, actors made up as different ape species tended to hang out together, gorillas with gorillas, orangutans with orangutans, chimps with chimps. It wasn't required, it just naturally happened.
Roddy McDowall, an experienced actor, recommended to his companions in makeup that they should frequently add tics, blinks and assorted facial gestures to add a sense of realism and keep the makeup from appearing "mask-like". McDowall reportedly became a merry prankster with the makeup, driving home with his make-up on, and shocking some of the other drivers on the freeway. While doing the La Planète des Singes (1974) television series, Roddy surprised Carol Burnett when he showed up on The Jackson Five and Roddy McDowell (1974) in full Galen makeup while she was taping her intro talking to the audience.
At one of the first test screenings, a woman walked up to Charlton Heston and asked how he was doing. Heston had no clue who she was until she revealed that she was Kim Hunter (Zira). He did not recognize her because he had not previously seen her without ape make-up.
All the ape actors and extras were required to wear their masks even during breaks and in between shots because it took so much time to make them up. Because of this, meals were liquified and drunk through straws.
The "See No Evil, Hear No Evil, Speak No Evil" gag was entirely ad-libbed on the set on the day of shooting. It was kept in because people found it amusing when the film was threatening to get too serious.