Continuity mistake: When Hughes is asking Ava about going to Paris, 2 guys with blue suits pass behind three times.
Continuity mistake: Before Flynn is thrown the paper ball, a couple passes behind him and disappears in the next shot.
Continuity mistake: When Howard Hughes is having a shave with Katharine Hepburn, he has shaving foam left on his chin from the shave. In the next shot when Hughes goes to wash his face, all the foam has disappeared.
Continuity mistake: The amount of fog during the Hercules presentation changes abruptly in barely half a second.
Continuity mistake: Errol Flynn is standing tall, then extends his hand to greet Hepburn and when he is almost touching her hand, the shot changes and now he is far away, hands out of reach and kneeling down.
Continuity mistake: When Howard Hughes is asking Mr. Mayer for two cameras, the people passing behind don't match between shots.
Continuity mistake: When Hughes is burning his clothes, his fringe appears in the close ups and disappears in the wide shots.
Visible crew/equipment: Lighting screens are reflected in Hepburn's glasses while she's in the car heading to the set.
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.
Deliberate mistake: During the flight Hughes takes with Katherine Hepburn, they talk to each other in normal, conversational voices. A twin-piston-engined aircraft of that vintage (or any vintage for that matter) is LOUD. We should be able to hear roaring engines, and the two should have to shout at each other to be heard.
Continuity mistake: When a model Hercules is shown in the party, the plane passes by two ladies in red twice.
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.
Visible crew/equipment: When Hughes is flying the new and faster airplane, you can see the filming crew reflected in the side of the plane. You can see it at full speed but you can see it better if you slow playback down a bit.
Continuity mistake: During the presentation, the position of the Hercules doesn't match in the close and wide shots.
Continuity mistake: After Noah Dietrich introduces himself for the first time, the shot changes and everything to the right disappears.
Continuity mistake: A drop of soap on the lower right side of the sink when Hughes cuts himself appears and disappears depending on the shot.
Continuity mistake: In the scene when Howard Hughes and his young girlfriend Faith Domergue are in the Coconut Grove meeting with Juan Trippe, Faith is seen with a sundae in front of her. In one shot, she's eating the sundae, and in the very next shot her hands are suddenly in her lap.
Continuity mistake: When Howard Hughes starts to shout "Oklahoma," the shadow of the tower behind him and Dietrich changes.
Continuity mistake: When Howard Hughes cries out "Oklahoma," he passes behind Dietrich and then in the wide shot he is behind him again, repeating the movement.
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. :)