What do you think Will's neighbor probably did before he left on his flight at the end of the movie? Hugged his children. So much for Infant Immortality.
Remember when Will was about to give his father the new ALZ-113 drug to permanently cure him of Alzheimer's but his father refuses it, prompting him to let him go. Later in the film, it's revealed that the drug is fatal to humans. If Will's father didn't refuse the drug at the last minute nor if Will didn't listened, he could have died a long painful death.
And Will would have been next.
Koba is probably the most vicious ape in the story, particularly toward his captors. When you realize that bonobos are one of the least aggressive species of ape (they'll fight if threatened, but they're nowhere near as psycho as chimpanzees), it makes you wonder: What were those scientists doing to him?
Now, I'm no medical expert but after seeing that humanity is doomed and likely to be wiped out by the virus I wondered... there were still humans in the Planet of the Apes, being hunted, right? Sure the humans were a bit slow, but what are they? Immune? Then I realized... the virus was meant to cure Alzheimers, and the human it was tested on was cured, only to soon revert. Medicines given to someone without a disease can cause problems or issues. So one might say that the disease is only fatal to regular humans, while those suffering from Alzheimers get cured for a time before reverting to their simple, more forgetful selves.
Trouble is, people with Alzheimers are usually too elderly to breed, meaning they're unlikely to be the ancestors of whatever future generations of intellectually-stunted humans remain. More likely, the plague will fall shy of a 100% mortality rate, but will leave any lucky survivors quite mentally damaged, and their children too.
The sequel says that the virus had a 99.8% mortality rate.
The final scene of the film where Koba wanted to kill Will for being a human (and one of the scientists of the company that experimented on him) and Caesar defending the latter perfectly foreshadowed the entire plot of the sequel.
Before running away, Bright Eyes tries to jump back into her cage. This act seems meaningless and is entirely forgetable if you don't rewatch, when you know baby Caesar is inside the cage.