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.
Answer: The first sections of the film are shot in two-strip and three-strip technicolor, a common practice in the early versions of color filmmaking that were happening at the time. The scene on the golf course between Howard and Kate Hepburn is a prime example. As far as the later sections of the film, never underestimate the power of digital effects. :)