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.
Continuity mistake: When a model Hercules is shown in the party, the plane passes by two ladies in red twice.
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.
Continuity mistake: At the end of the scene in the Coconut Grove, with Howard Hughes and his young girlfriend, Faith, eating a sundae, Howard's arm switches between shots from being over Faith's shoulder, to in front of him. He is seen in one shot removing his arm from her shoulder and wiping his hand because he shook Juan Trippe's hand. In the next shot his arm is over Faith's shoulder again, and in the shot after that, he is wiping his hand again.
Continuity mistake: After the plane crash, when Hughes is lying on the floor we see his left trouser is undamaged, but a second later it's in rags and the part going from the knee to the foot is missing.
Continuity mistake: When Hughes takes off to fly (and crash), a huge zebra crossing magically appears on the concrete.
Continuity mistake: Before Flynn is hit by the ball, he is holding a drink and cigarette. After the hit, they swap hands in less than half a second.
Continuity mistake: After Ava Gardner shaves Howard, she instructs him to wash off his face. He looks at the sink and all of the water drains out. Then there is a shot over the sink as he is about to rinse off his face with a lot of water in the sink. It should still be empty. (02:14:55)
Continuity mistake: When the mother is washing young Hughes, she places her left hand close to his neck and pulls it back, leaving just the tip of her fingers touching, but from a different angle all of her hand is still on his neck.
Continuity mistake: When the Hercules first flies, the boats on the water below suddenly disappear.
Continuity mistake: When the Hercules model is coming in, the propellers are spinning, but as the model passes the camera, they aren't. Once the Hercules model has passed the camera, they are spinning again.
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. :)