"Mr. Howard, 'auditory' doesn't mean he put shoes on his hands, it- OK, you don't care."
The movie completely ignores the fact that John and his wife divorced in 1963, just six years after being married, and never got remarried until 2001 (in addition to the whole insanity thing, the fact that the real Nash dabbled in boning dudes probably didn't help their marriage either). The film also manages to not mention his anti-Semitism, which the real Nash says must have been a side effect of his illness.
At the end of the film, Nash mentions to a friend that he is taking new medication, and he makes a heartfelt speech dedicated to his wife when he accepts his Nobel Prize.
The truth, however, is that both of those things were complete fabrications. Nash stopped taking any medication in 1970, and his continued instability--probably in large part due to that refusal to take medication--led to his not being allowed to make an acceptance speech for fear that he might whip out his dick and start screaming racial slurs at imaginary Jews.
So while the real Nash probably wouldn't have made the best protagonist of a Ron Howard film, we're definitely adding him to our list of "Celebrities Who Need to Get on Twitter."