These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Planet of the Apes 2001: Nothing explains how the horses came to the planet in the 2001 remake.
Or, for that matter, how the ape population grew as large as it did when there are relatively few apes on Leo's ship. However, it's implied from the ship's log that the surviving scientists used genetic manipulation to make the apes what they became in the film. It's possible they increased the breeding process as well.
Even that wouldn't account for the presence of gorillas and orangutans, which are substantially larger than chimps and thus, a very poor choice for a space mission where food, water, oxygen and living space are all at a premium. Not to mention that sending apes to space is already Zeerust, as NASA quite using non-human primates as soon as they were sure it was feasible to bring humans back safely.
Planet Of the Apes 1968: The chronometer showing Earth time is still working after the rest of the ship's power fails (in plot terms, Taylor has to see it immediately before he leaves the ship).
Escape from the Planet of the Apes: The humans learn that in the future, apes will talk and treat humans like animals. So they want to prevent Cornelius and Zira from having descendants as their descendants would probably be talking apes. They fail. But does this mean that Cornelius and Zira are their own ancestors?
No, because the origin story they told (of an ape slave who one day said to humans what had been said to him a thousand times over - "no") is different from what came to be after they traveled back in time - their son Milo/Caesar became the savior of the apes instead.
Probably not. Other chimps evolve by the time of the next film, after all.
And their son, Milo who becomes Caesar in that next filmloses his son by the time of the fifth and final Ape movie. It doesn't say he and his wife had more children.
On another point, it strains credibility (to say the least) that Dr. Milo would be able to raise Taylor's ship from the lakebed, refit its blown hatches and get it working again, just in time to escape the Earth's destruction. Of course, without that rather huge implausibility there'd be no movie, so...
"Funny Aneurysm" Moment: Roddy McDowall (Cornelius) was reluctant to take the part, because he was worried that no-one would recognize him under all that make-up. Instead, he became the only actor to appear in all the sequelsnote though only in archive footage in Beneath as he was busy and TV series, and (unfortunately) is all most people remember him for.
Hell Is That Noise: In the TV series, hoofbeats, as that can only mean that gorilla soldiers are approaching.
Hilarious in Hindsight: Seeing the future NRA president heft a shotgun and declare "I'm pretty handy with this!"
All the budget for ape prosthetics in Beneath clearly went into the full-body suits for Zaius and Ursus, along with Cornelius and Zira. As a result, the remaining prosthetics range from mediocre to downright awful, especially in the scenes showing large crowds of apes.
Milo repeatedly saying "Mama!" at the end of Escape is very obviously a short clip of a chimpanzee being played forwards and backwards repeatedly, and can serve as a source of Narm for an otherwise tragic scene.
It can be argued that Taylor blew up the entire planet because of Zaius' hypocritical viewpoint that humans are violent... just as an army of apes shoot Brent.
Tear Jerker: Cornelius and Zira's deaths. The most likeable, human characters in the entire series.
They Just Didn't Care: The TV series was determined to exemplify this trope. We see ape surgeons wearing surgical masks, which indicates that they understand modern germ theory...except that, in "The Cure," they suddenly don't. Again, we see an ape wearing spectacles, so they must have some basic knowledge about glass-making, optics and lens grinding. Well, until Galen has suddenly never seen glass or heard of a magnifier. They've got advanced metal-working skills, but have never heard of fish nets. The list goes on.
Partially explainable by the Schizo Tech invoked due to the Science Is Bad beliefs of the orang-outangs — for example, in "The Surgeon" (the above-mentioned episode featuring surgeons in surgical masks), the apes haven't identified basic blood types and Galen is able to fake being a doctor by seriously discussing the medicinal qualities of bleeding patients with leeches. Plus, "apeworld" is provincal; out in the boonies, things are a lot simpler, while closer to Capital City technology tends to be higher.
Fridge Brilliance: In the TV series, the origin of the Ape civilisation is that they evolved full sapience after humanity destroyed itself and took over. While they purposefully eradicated the true history, it's quite logical that they stole as much human-knowledge as they could to build their own empire. Add the orang-outang conspiracy to keep the true history of the world hidden from the apes, and, naturally, much of their technology falls under Monkey See, Monkey Do — they're imitating human knowledge as best they can without knowing or understanding why something is done. Ape doctors wear germ masks because they're, without knowing it, aping human doctors — they don't know that the masks prevent infection, they just know that "this is the way it's done".
Values Dissonance: In-universe example in the TV series. In "The Gladiators," Burke refuses to kill Tolar after he defeats him in the ring. Tolar is furious.