Shown Their Work: Possibly. A leading theory for the cause of the rapid spread of AIDS in North America is "a promiscuous flight attendant". With even more air travel, and an easier route of transmission, the spread isn't that hard to believe.
Rocket makes noise with a gas can to reinforce his position as leader. Later, Caesar uses the same gas can to hit Rocket, and ends becoming new leader of the sanctuary. This is reminiscent of a real case studied by Jane Goodall, where a clever young chimp realized that the noise made with a gas can scared the other chimps and used it to become the tribe's leader.
They also had earlier drafts with a sympathetic vet character (named Stewart, after the unlucky female astronaut in the first film) working at the lab who becomes involved with Will, but this was later replaced by the zoo vet character. Before the character of Will's father with Alzheimer's, there was a draft with the lead humans being a geneticist and his wife with the disease.
The most ironic part is that the first script wasn't even written as part of the Planet of the Apes franchise but was based on reports of real people raising chimps as pets (or babies) and then getting mauled in their homes when they become teenagers. The first incarnation of what would become Caesar was evil and talked only in sign language; its genre was probably closer to a sci-fi horror than the drama/adventure movie it ended being.
Will died in the first cut of the film, but test audiences didn't like it.