Continuity mistake: When John's wife is in the bathroom she drinks all of the water in a cup, but when she throws it the cup is full again. (01:29:00)
Other mistake: When Nash is put into the car and is being taken away to the hospital, there is a line of people watching him drive away. Two of the spectators are the imaginary roommate and the little girl. They are standing in front of rest of the spectators. As the car is driving away you see a female student look around the imaginary roommate to see the moving car. If the roommate can only be seen by Nash why did she need to look around the roommate to watch the car drive away?
Factual error: The baby's pacifier that was used was not made at that time. It looked more like a NUK than the old rounded rubber tip.
Continuity mistake: In one of the first scenes where Nash is being introduced to everyone around the punchbowl, the trees around them have CGI leaves added on since it was shot in January and had to look like early fall. In shots that show the trees' shadows on building walls, all we see is branches. Shouldn't there be leaves?
Factual error: Mid movie, they show a Timex wall clock. But Timex did not make synchronized wall clocks. Simplex did.
Factual error: During the car chase, a rear window brake light is visible in John's car as he looks back at his pursuers. These devices weren't invented until the 1980s.
Continuity mistake: When the student approaches Prof. Nash in the Princeton library, he tells Prof. Nash he has been working on a mathematical theory. When the student hands Prof. Nash what appears to be a binder he does so by holding the binder with his left hand, palm down and fingers on top of the binder. In the immediately subsequent shot of both Prof. Nash and the student, Prof. Nash takes the binder from the student who is now holding the binder palm up, fingers under the binder.