Nash's breakthrough to acknowledging his schizophrenia: he realizes Marcie has never aged in all the years he's known her.
Ron Howard brings up one for Russell Crowe in his commentary, for the scene where he writes a complex equation on the chalkboard while talking. Just try talking while writing something that's different from what you're saying to get an idea of how hard this is.
Nash and his imaginary friend threw a desk out the window. Nash was barely affected, his friend was winded hard. This means Nash picked up a heavy desk and threw it out by himself. If any of that actually happened...
