Continuity: Franciscus' character arrives at a New York City subway station called Queensborough Plaza. Queensborough Plaza is an above ground station. Queens Plaza is the name of an underground station in New York City.  (They are located within walking distance of each other, but are definitely distinct stations).

Factual error: Brent enters the underground area via Queensborough Plaza. He and Nova walk some distance through (sewers?) and emerge outside the main branch of the New York Public Library, located on 5th Avenue and 41st St. in Manhattan. I'll concede that that's possible, since we don't really know how much tunnel they walked through. (It's about 2 miles and includes crossing the East River.) Only moments later, they're in front of the New York Stock Exchange, which is at 20 Broad Street, easily four miles to the south. In the next shot they're walking past Radio City Music Hall, on 6th Avenue and 50th Street. That's roughly a half-mile NORTH of the Library. I know stuff got shook up in the nuclear blast, but that's a bit much...

Revealing: When Brent is attempting to get the reins for the horses after escaping his wheeled cell, you can see a second set of reins going through the wooden holes to where a driver is hidden. When he gets the fallen reins, the second set is no longer there.

Revealing: When Ursus is giving his speech in the Ape city, many of the Chimpanzees and Orang-utans are wearing incredibly fake-looking masks.

Continuity: When the Apes are trying to break into the mutant's church, Mendez looks towards the Alpha/Omega bomb, and is wearing a cream-colored jumpsuit with a purple sash. When the Apes do break in, his sash has disappeared.