First, remember that the movie, while based on the book, is not a biography. There's a great deal more to the story of Dr. Nash and his family, to his mental illness, and to his discoveries. Significant parts of the movie are fiction, or are based on related events that were combined or, ah, adjusted for dramatic effect.
His real story is fascinating, but would probably not translate well into a movie.
Second, Dr. Nash's theories on gamesmanship and related economics were originally developed in his younger years (late 1940's to early 1950's), before his illness to significant effect (and again, not at all as portrayed), circa 1959. Did the illness affect his reasoning at that time? One wonders. Does that make his reasoning fallacious? Not neccesarily.
Third, and most importantly, the discoveries in question date back to the 1940's. Not the 1970's. If you look at some of his listed works on the
Wikipedia entry, you'll see that the published dates start off in the 1950 - 1953 era. And while he may have credit for these theorums, many others have worked on them, and published other insights based on them, after.
So, did our economists adopt a flawed theory from a mad man? Was the theory flawed? Did they actually implement his theory? Was he mad at the time? Those are the questions we must first answer before the main question can be evaluated.