Continuity mistake: Near the beginning of the film where Howard Hughes flight tests the silver monoplane (the H-1), the close up shots show an open cockpit while the longer shots show a closed cockpit.
Revealing mistake: During the filming of 'Hell's Angels' Howard gets the idea to build a single wing mono plane. He and another take an axe and smash the support holding up the upper wing. If you notice the upper wing is already broken, hinged and a very poor covering has been laid over the joint. It is very obvious and noticeable in a few shots leading up to this.
Continuity mistake: During lunch with the Senator, the vegetables and potatoes on Hughes' fish change between the first and second shot.
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.