Revealing mistake: Early in the film, when Hughes and another guy are walking past one of the replica WW1 aircraft used for the "Hell's Angel" scenes, you can see the ends of the cylinders of the modern air cooled engines they used to power it. The original aircraft (SE-5A) used a water cooled V8 which wouldn't have been visible.
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.
Revealing mistake: When Leonardo DiCaprio is wiping blood off his hands in the bathroom scene, you can tell the blood doesn't really come from cuts. It's just fake blood they put on his hands for that scene.
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.