Deliberate mistake: In the orphanage scene, Santa's bag drops dead center in the fireplace. The noise of the impact gets baby Buddy's attention in a quick shot, and the camera shifts back to the fireplace. Now, the bag has shifted to the viewer's left when Santa's boots are coming down. The shift of the bag is presumably to make room for the boots coming down the chimney.
Deliberate mistake: When the penguin goes into the cemetery, he bumps a tombstone and it moves. Almost certainly a tribute to legendarily poor director Ed Wood, who Tim Burton later directed a biopic of - this exact thing happened in one of his films. (00:39:15)
Deliberate mistake: When Rocky cuts Drago during round two of their fight, the punch actually hits Drago on the chin. His eye would not cut from that impact.
Deliberate mistake: When the terrorists shoot a man in the church and he falls on his back, both benches behind him topple (in the shot from the ceiling of the church). You can't see that the benches are connected and even if they were, the bench he doesn't actually touch wouldn't topple. (00:07:35)
Deliberate mistake: During the scene with the malfunctioning juice maker, when it goes nuts there is no possible way that all that juice and pulp could have come from just one orange. (00:22:45)
Deliberate mistake: Jack Lemmon looks at his watch as he puts his thermometer in his mouth, and when he takes it out. Obviously in 25 seconds a 1960 mercury thermometer would not give a reading of his 101 fever, it's deliberately done for the scene to move on (although it could have been done differently, with a cut or having him retrieve the thermometer later, since the scene is static and lasts much longer, enough for a real thermometer to work). (00:19:20)
Deliberate mistake: At the end of the film, two officers attempt to surround and handcuff Joshua. Using two officers to cuff someone is NEVER done for the exact reason of what ends up happening, as Joshua manages to grab a gun from one of the officers. Only one officer would have been doing the deed in the real world, but it's clear this error in being completely against police protocol had to happen so the good guys could prevail over the villain.
Deliberate mistake: Gonzo and Rizzo are selling apples in the beginning, including the Red Delicious cultivar. That wasn't invented until the 1880s and the story is set sometime in the first half of the 1800s. Most likely intentional as they are the narrators.
Deliberate mistake: In the beginning Chris and Jaime are on the bed talking and she is excited about graduating she is wearing a mini dress. In the shot where she falls face down in his lap and her dress goes up, she's wearing black tights underneath her dress, which are not there in any other shot.
Deliberate mistake: For Hans Gruber's iconic death scene, Alan Rickman's fall was filmed at high speed (for slow-motion playback) against a green screen, and the skyscraper perspective footage was added later as background. However, while Rickman falls away from the camera in slow motion, papers are fluttering around him in the background at normal speed. This was done deliberately to make the shot even more surreal.
Deliberate mistake: Near the end, after the case is dismissed, people are celebrating, and we see a reporter talking, with snow flying around him. Cut to another shot of people watching a television. The snow has disappeared from the reporter's shot. It's likely that, since the snow was added in post, the filmmakers forgot to include it in that one shot.
Deliberate mistake: In the end scene at the TV set, Scrooge tosses a coin out the window, and the camera follows the coin as it falls in slow motion. The people in the control room also watch this on their monitors. Problem is, this is a live broadcast and filming/watching something live in slow motion is impossible.