Deliberate mistake: The morning after the flyers are spread, Buster is sleeping in a drawer. When his alarm clock goes off, he hits his head at the top of the drawer, but later on, he can be seen standing up in it, easily visible when he is putting his coat on. The drawer obviously became wider for him to stand up in it.
Deliberate mistake: After David jumps off the roof of the Firebrand building, it is discovered that he had been wearing a parachute, but this parachute was never visible on him at any point previously in the scene. Even when he was on the roof and after jumping, the parachute was nowhere to be seen. The parachute was too big to have gone unnoticed. It would have been visible whenever the shot was behind him and the straps would have been seen whenever the camera was in front of him. (01:17:30)
Deliberate mistake: Some odd legal matter must be involved here; when we see the two ladies look at the viral video, one tells the other to look at the "Youtube" sensation with over a million views, but the website shown is not Youtube but an obvious knockoff version. (01:19:30)
Deliberate mistake: The movie is set in the late 50s, but Howard Hughes is dealing with his plane crash and the senate hearing about the H-4 Hercules prototype. Those are events from over a decade earlier. However, it should be noted that the initial disclaimer of the movie is "Names and dates have been changed."