Continuity mistake: In the scene on the Golden Gate Bridge when the apes are pushing the bus, the police shoot the bus numerous times, but when the camera goes off the bus and then shows the bus again (twice) the bullet holes are not there anymore.
Continuity mistake: When Will tosses the envelope with money on the table, it moves away/closer to the stack of papers, depending on the angle.
Revealing mistake: When the apes jump out of the lab windows out to the street, they don't cast a shadow on any of the glass except the ones on the ground floor.
Factual error: At the end of the film the apes/monkeys are seen jumping clean through the EXTERIOR windows of a downtown high-rise. I know apes/monkeys are a bit stronger than humans, but this is still is highly unlikely and would not happen so easily. The exterior windows (those from floor to ceiling, or those that replace traditional exterior walls) would be triple plated, like that of a bank partition (think of 3 car windshields glued together) One would have to repeatedly bang on it with a sledgehammer before it would even crack, let along jump clean through. However, jumping through the INTERIOR windows and doors are completely realistic since those would only be double plated.
Continuity mistake: In the scene where the chopper with Jacob fly to the bridge, they shoot and kill many apes. But only moments later when Will gets into the police car to pursue Caesar, he drives through the same section of the bridge and there are no dead ape bodies nor are there any traces of blood or anything.
Continuity mistake: The fog on the bridge at the end sequence varies greatly from very thick (when on the ground looking from behind the police) to very thin from aerial shots to almost non existent in some overhead shots.
Continuity mistake: When the apes are about to break into the lab, there's one way ahead of them jumping against the glass. A frame later, when the angle changes from inside the premises, there's suddenly a bunch of apes very close to him.
Continuity mistake: The number of primates running around at the end of the movie seems to be exponentially larger than the amount of them that were in the zoo and the sanctuary.
Continuity mistake: When they are entering the Redwoods for the first time, you can see that Caesar's leash changes all the time in length and position.
Continuity mistake: During the big face off on the Golden Gate, Caesar climbs on the roof of a black Nissan and signals the apes to halt. In the next shot, the car is now a Volkswagen. (01:24:45)
Continuity mistake: After Will tosses the money at a man, his right arm is either on the table or down, depending on the angle.
Continuity mistake: Mr Jacobs enters the building invaded by apes. There's a fallen table right behind him. He turns around 180ยบ to watch the apes but in the immediate wide angle the table is still behind him. He should be facing it now.
Continuity mistake: When Dotti sees Mr Franklin dead, his hand is laying on the center of a white stripe on the blanket. In the immediate close-up it has moved several centimeters to the left.
Revealing mistake: When Will's dad's Alzheimer boosts and he smashes the car driving in reverse, the headlight of the car behind is blatantly loose to increase the drama of the crash.
Factual error: The car tags are the same color even after many years Caesar is born. Three years after and then five years, the car tags are still yellow.
Suggested correction: Car tags use a very small number of colors for their stickers. Blue, green, red, orange, yellow are the primarily used colors for registration tags in California, and after some years they start to get used again. Of course the tag colors change year to year, but it is completely plausible that the same color could be used again in the 8 year span that you mention.