Factual error: When Hughes flies the open cockpit H-1 at over 350mph he isn't wearing goggles. There isn't a sign of any wind at all in the cockpit. Even with a windscreen, the wind would cause your eyes to water well before 350mph.
Factual error: While in the air shooting scenes for Hell's Angels, a camera mounted on a wing breaks and film flies out. The film is brown in color, the hue of undeveloped color film, and Hell's Angels was obviously filmed in black and white. The film should've been grey or blue as this is the color of undeveloped black and white film.
Factual error: In the 1940ish Connecticut scenes of the Hepburn family, one member was taking movies with a Bolex reflex movie camera not manufactured until the late 1950s.
Factual error: Some of the glasses in the film are too thin and modern to belong to the time period, such as the ones that Robert Gross wears. As well, his lenses, as well as those of Senator Brewster, reflect light with the distinctive iridescent green/purple of non-reflective coating, which was not available back then.
Factual error: Howard asks for ten chocolate chip cookies in a scene set in 1928. Chocolate chip cookies didn't exist until 1933, and they were known as "Toll House" cookies then. The generic term "chocolate chip" wasn't coined until the early 1960s.
Factual error: When Hughes flies (and crashes) the first XF-11 prototype the plane has the wrong markings - a U.S. insignia with a red bar. This red bar was added in 1947 (to all planes, including the second XF-11 prototype), the year after the first prototype test, after the U.S. Army Air Forces became the U.S. Air Force.
Chosen answer: Hughes has obsessive compulsive disorder. He washes his hands so often, and so intensely, that he's literally worn away his skin. This is common with OCD sufferers.