Deliberate mistake: In the scene at the start of the movie with the "authentic" piece of film, you can see a girl with a hat waving to the people at the ground. When the ship is leaving port in the film, she and others are in the same positions, only in reverse, because the first "authentic" shot is the same shot, only mirrored. (00:00:40 - 00:25:30)
Deliberate mistake: At the end of the movie Rocketman shows his lady friend a space blanket, out of which he states he made something: ballroom dancing outfits. The difference in the material is just too obvious for this not to be a deliberate mistake. The outfits aren't the slightest bit related to the foil they were supposed to be made of.
Deliberate mistake: Every time George swings into a tree, there is a George shaped impression created. However, in the next scene the tree is back to its natural shape.
Deliberate mistake: It's a humorous twist that Randy's killing is covered up by some random guys passing by with a ghetto blaster, but there was dead silence when Randy was talking earlier; not being in frame does not block soundwaves. (01:05:15)
Deliberate mistake: In the very first shot of Korben Dallas, his bedside clock is facing away from him, towards us. We can read it, but he shouldn't be able to because he'd be looking at it backwards.