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."
Rules Don't Apply (2016)
1 deliberate mistake - chronological order
Directed by: Warren Beatty
Starring: Paul Sorvino, Ivar Brogger, Peter Mackenzie, Steve Tom
Continuity mistake: The protagonist is on the couch with his girlfriend in Fresno. He mumbles worried about her dad "knowing"; his hands are joined with different placement (left on top, right on top) between shots. (00:13:15)