Corrected entry: When Yeager hits Mach 1 and the X1 is vibrating, the windscreen cracks. Very dramatic, and totally untrue; nothing of the sort happened. At that altitude the cockpit would have explosively decompressed if the windscreen had given way.
Corrected entry: When Sam Shepard is dropped from the B-29 mothership he hits four switches to fire the rocket engines that are all right next to each other. The real X-1 had the switches for each rocket engine located far more apart from each other making it impossible to throw them all at once.
Correction: http://www.dfrc.nasa.gov/Gallery/Photo/X-1/Medium/E49-00010.jpg - The four switches in the lower left (2 are hidden) are the ones in question. It looks like they got it right.
Correction: The film does not show the canopy breaking during the X-1 flight when he breaks Mach 1. Gauges crack, But the canopy remains intact. However, during his X1a flight he did, in fact, hit his head on the canopy and broke it. This is depicted correctly in the film.