Science Marches On: the film makes it clear that Ape society is composed of all (non-Human) apes: chimpanzees, gorillas and orangutans. Back when the film was made, bonobos were thought to be chimpanzees, but nowadays they're known to be a separate species.
This leads to some Fridge Horror: if bonobos are not present at all, it means they all died at some point (How? By whom?); on the other hand, if they're still around, given that we don't see them in the movies and the most notorious aspect of their society, it's not unreasonable to assume they are sex slaves, imprisoned in the homes of the other apes.
Throw It In: Taylor's final rant at the end was thought up and written down by Charlton Heston on the day of shooting that scene. It adds much more power to that Wham Shot, even after repeat viewings.
Zaius was originally going to be played by Edward G. Robinson, but his ill health did not mix well with the heavy makeup, and the part had to go to Maurice Evans.
Also, Linda Harrison played Zira in early makeup test footage, but was later cast as the human Nova. (Both roles are due to dating the the studio head, but her former beauty pageant looks helped with the latter.)
The early scripts for the movie had a closer resemblence to Pierre Boulle's novel, but budget constraints forced the change to the primitive ape society of the film.
Interestingly, there was a sort of segregation behind the scenes during filming; the chimpanzee actors ate with other chimps, gorillas with gorillas, and orangutans with orangutans.
Once, some of the gorilla actors rode from the makeup area to the set in a convertible with the top down, wearing their full gorilla makeup, wigging out some observers on the way.
The Statue of Liberty scene was based on a scene from an earlier sci-fi story.
Regarding the sequels
Real-Life Relative: Along with the wife of the studio president (Linda Harrison, Nova), Beneath had the wife of producer Arthur P. Jacobs, Natalie Trundy, as a female mutant. Trundy returned in the other three, as a veterinarian in Escape and Caesar's wife in the last two.
Pierre Boule wrote a sequel draft called "Planet of the Men", which can be seen at Hunter's POTA Archive website (just Google it). It involves Nova and Taylor having a son named Sirius, who eventually leads a human uprising. The apes lose their intelligence and are back to being animals by the end. The last scene has Zaius doing tricks in a cage in a circus.
An early concept for "Beneath", if Heston had allowed Taylor to have a bigger part, would have ended with him still alive and helping with a mixed school of ape and human children. The Sequel Hook was a trio of mutant gorillas emerging from a hole in the Forbidden Zone and symbolically shooting a dove.
Taylor was supposed to be the main character. But since Heston only accepted a smaller role which ended with Taylor dying, the script was rewritten to feature Brent. Also, Taylor, Nova, and Brent were meant to survive and help establish peaceful relations between the humans and the surviving apes.
Makeup for a hybrid child was tested for "Beneath", but dropped due to fears of reactions about the bestiality insinuations.
Said site also has script ideas from other attempts at Apes movies. There was a concept about a scientist traveling to the past to fight the apes and prevent a biological time-bomb from destroying humanity in the present day, and a concept that was similar to Boulle's novel, with humans traveling to a planet of apes essentially imitating the ideas they got in signals from Earth.
Some of the gaps between Conquest and Battle were filled in by a 2005 six issue comic called Revolution on the Planet of the Apes. It also contains some short storires,several of which fill in more of Caesar's backround and several set in the gap between Battle and the original film, obviously trying to bolster the circular timeline theory.
Conquest was well liked by African-Americans, who saw it as an allegory for their own struggles. The riot in the film was actually inspired by a real-life African-American riot.
The original cut of Conquest does not have the last few of Caesar's lines, instead ending with his shout of "That day is upon you NOW!". Roddy McDowall was asked to dub a few more lines to try and lighten the film's dark tone.
Battle similarly had some stuff edited out, that, when put back, blatantly bolsters the circular timeline. There are scenes of the start of the mutant society from Beneath and a bit more involving the bomb.
Regarding the TV series
Canon Discontinuity: The films are admant about how all dogs and cats were killed by a plague. But, in the TV series, what do the astronauts see in one episode? Yep, a dog. Someone must not've been paying attention to the films closely. (Although it isn't out of the realm of possibility that a few animals could've been immune…)
Edited for Syndication: Some of the hour long episodes were edited together for local tv reruns as two hour 'movies'.
Missing Episode: "The Liberator" didn't air in the United States during the original run. This is due to the controversy of its plot, which culminates in a man stockpiling chemical weapons (crude poison gas bombs) in hopes of using them to wipe out the apes who oppress his village.
Actor Allusion: Charlton Heston is an ape, and Linda Harrison (Nova) also cameos. Charlton Heston's character bemoaning the human invention of guns (keep in mind this was near the end of Heston's tenure as president of the National Rifle Association).
All-Star Cast: Mark Wahlberg, Tim Roth, Helena Bonham Carter, Michael Clarke Duncan, Paul Giamatti, Kris Kristofferson.
While in Development Hell, several people were attached at various points and vastly different scripts were considered. Had the project been greenlighted at any moment between 1988 and 1999, the movie would have been completely different from Burton's version (except for the apes' makeup: Rick Baker was practically attached from beginning to end). To recapitulate:
Adam Rifkin's idea (1988): An alternate sequel to the first film, set centuries later, where the Apes have a Romanesque civilization and use humans as slave labor. A descendant of Taylor played by either Tom Cruise or Charlie Sheen would lead a human revolt.
Sam Hamm's script, in collaboration with Chris Columbus (1995): A closer movie to Pierre Boulle's novel, where Schwarzenegger would play an astronaut instead, and the apes lived indeed in a different planet and had a highly-advanced civilization. Almost all of it, however, would be either taken from once advanced ancient humans from the same planet that had wiped themselves out in a war in the distant past, or from TV transmisions from Earth that the orangutans had caught in secret before introducing all the advancements featured as if they were their own inventions, in order to justify their privileged status.
James Cameron's idea (1996): An Alternate History of the original saga, where the orangutans had been overthrown by the chimpanzees prior to Taylor's arrival and developed as a result a more advanced civilization. It would begin with original footage from the first film before introducing a second astronaut landing years later, and culminate with the new protagonist meeting Taylor (played by Charlton Heston, of course), now the old founder and leader of a tribe of intelligent humans.
Tim Burton's take itself went through different rewrites, having originally an Ari that was an "ape princess" rather than the daughter of a senator, Thade as an albino gorilla, Limbo making an emotional Heel-Face Turn instead of remaining a jerk, and Leo crashlanding in New York during his return to Earth instead of in Washington, D.C.
Word of God: From one of the actors (as opposed to the usual writer or director), Helena Bonham Carter stated that the ending was "...all a time warp thing. He's gone back and he realizes Thade's beat him there." When one considers that Leo's craft was still in the lake and could be retrieved, this explanation makes sense.