Deliberate mistake: At the end of the film, Gaston shoots the Beast with an arrow and pushes the Beast out the window. When the Beast lands on the edge of the castle rooftop, the arrow has disappeared. Even if part of the arrow has broken off, a piece of it would still be in his back. [This, like many other incidents in the film, is a longtime Disney animated tradition. The company seems to believe that violence is less unpleasant if all evidence of it disappears quickly. This is why so many cuts seem to disappear or become less serious. The arrow vanishing is just another example.] (01:16:55)
Deliberate mistake: At the beginning, the carolers are on the porch singing. The camera never pans, so this means that the carolers are facing away from the house (towards Gate) - seems rather odd. The only reasons for this would have been to make the clean camera move through the crowd and up the house.
Deliberate mistake: In the scene where T& L are being pulled over for speeding, when they park, you see no protective rails on the side of the street they are on, but after they put the officer in the trunk and return to their car, on the passenger side, the rails are very visible.
Deliberate mistake: Marian is wearing pantaloons, or knickers, in the rape scene. Knickers were not worn by women until Victorian times, and then they were split at the crotch.
Deliberate mistake: When Ed's looking at the drawings done by the sketch artist near the start, he's flipping over a book of them. Trouble is that they all end up facing the camera, meaning that Ed must have been looking at the blank side - we see the blank pages briefly as he flips them. (00:14:30)
Deliberate mistake: When Cliff crashes into the pond after his first flight, Peevy tells him that he has to look around with his eyes and steer by moving his head. However, just before this as he is flying next to the passenger airplane, he looks over at it, turning his head to the left without changing directions at all.
Deliberate mistake: When everyone is surfing at night, the sound of the waves in the background is significant, as it should be. However, at one point, when Keanu and Lori are having an intimate conversation on the water, the sound of the waves disappear. The wave sounds resume in the next scene.
Deliberate mistake: It's not particularly believable that the away team to stop the assassination would consist of the ship's entire senior staff, and raises the question of who was left in charge of the bridge (the answer: apparently nobody, as they return to a completely deserted bridge). Of course this is dramatic license, and at this point the audience won't care or likely even notice.
Deliberate mistake: The number of acts Lecter performed during his escape from the individual jail cell and until he was attended to by an officer (who thought he was an injured officer) would have taken a lot of time and effort to complete - way more time than he could have gone undetected by one of the many officers in the building. Slashing/ bludgeoning to death a person can be done fairly quickly (munching on a victim's face adds time!), but three particular acts required a substantial amount of time, especially for an elderly man whose ultimate goal was escape: Swapping clothes (undressing and dressing) with a police officer and trimming off his face/scalp to appear to be that officer, then getting to a strategic location to be discovered; Setting a dead officer on the roof of the elevator; and, somehow hanging / impaling (crucifixion-style) an officer from the top of the jail cell (which appeared to be around 10' high). The latter feat would be challenging for TWO physically-fit officers.