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.
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.
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