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: 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: 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)
Chosen answer: No they most certainly did not. That wouldn't remotely be considered a particularly respectful homage! They picked Alzheimers because it's specifically a brain condition, which can then be explored in the movie as a plausible way of explaining the intelligence raising properties of the drug used.
GalahadFairlight