Deliberate mistake: At the beginning of the Fellowship's journey, they are resting on a hilltop (Hollin) with rocky formations. Bill the pony is tethered in the background in one shot. Then come the spying crows from Saruman and they all quickly hide. When the crows swoop in closer we see no-one, but who hid the pony and where? (01:37:45)
Deliberate mistake: When Boo laughs repeatedly while playing hide-n-seek with Sully in the men's room, nothing happens to the electricity - no surges as with all other times she laughs. [In the audio commentary by the directors, they explained that it would've been distracting if an energy surge occurred every time Boo laughed, so they simply didn't address the issue. A reasonable course of action, but still a mistake.] (00:37:30)
Deliberate mistake: When her father jumps on the brakes, they lock up, even though the car is supposed to have ABS, which is supposed to prevent this from happening.
Deliberate mistake: According to the DVD version, the Army of Anubis roars in ARABIC. Rather strange for a monstrous army of an ancient Egyptian god... (01:44:15)
Deliberate mistake: Throughout the movie, you can see the size of true-size Rosemary, particularly her waist and legs. Notice the size of undies she was going to purchase when she and Hal first meet. Notice the size of her bathing suit bottom. However, in the scene where she throws her purple nightie undies at Hal and he catches them: the panties are WAY TOO BIG. Especially the leg holes, which could go around her true-size waist.
Deliberate mistake: Just after arriving in the 21st century, Thibault and André enter an elevator and scare away its occupants. Attempting to chase them, the elevator doors close despite their attempts to keep it open. Elevators have a safety mechanism which opens the door when they encounter resistance. This was ignored deliberately in the film for comic effect.