Deliberate mistake: At the end of the movie when everyone is on the bridge, the one female cop roundhouses the bad guy, who is clearly a white male in his 50's, but his stunt double is an Asian man (with different colored hair). They use the same stunt man a few other times for people he doesn't even look like.
Deliberate mistake: In the first bowling scene, all the lane numbers are backwards.
Deliberate mistake: During the movie, when Mulan is just a girl, you can see that her eyelashes extend beyond her eyes. When she is pretending to be a boy, her eyelashes are short (this makes perfect sense). But when she is in the medical tent her eyelashes are long even though she had no time to put on makeup. This is deliberate though, because without it she would have still looked like a boy, and just pulling her hair down wouldn't make her look any different (since that's how she looked in the pond). So they had to change her eyelashes to make her look more girlish.
Deliberate mistake: When the CA. trooper is at the front of her car, the Arizona license plate is shown. In 1989, Arizona began issuing a single license plate and that plate is always on the back of the vehicle. This is deliberate, as the remake follows the original movie shot by shot, and there the trooper checks the front license plate.
Deliberate mistake: Before the two shuttles dock to the MIR station, Lev initiates a rotation to simulate gravity. The shuttles then dock with their side hatch pointing to the anchorage. As the gravity is pointing away from the centre of revolution and the station is revolving around its main corridor, the gravity would push the astronauts back in to the shuttle and not towards the floor of the gangways leading to the shuttle or towards the floor of the shuttle. Also, the artificial gravity would be reduced to almost nothing at the main corridor. But here the artificial gravity somehow points down in every part of the station, and appears to work equally well throughout the station. (01:09:40)
Deliberate mistake: When Gregor is holding a long lens camera in a cafe house, he is pointing it at two men, you can see this when he looks through the lens, yet the next shot of through the lens is not from his camera but more like from a person standing right next to the two men. (00:59:40)
Deliberate mistake: When Riggs is chasing the guy on foot, you can clearly see it is a stunt double, who is also very apparent in other shots throughout the film.
Deliberate mistake: While Laurence is driving to the park trying to find Martha there are closeups of his car en route, and one of the closeups of the front left side of his car is a flipped shot, note the backwards "Saab" and the surface damage which is actually at the right side of his car. (00:56:00)
Deliberate mistake: At one point during the big escape chase scene, Finnegan takes a turn and the jet-ski he and Trillian are on side-swipes a wall and it's clear that they're about to fall off. The film cuts away briefly and then we see them and they're zooming along again as though nothing happened. The scene is portrayed in real-time so there's no way they had time to spill, get back up again and build up enough speed in the time between edits. Slightly sloppy editing. (And this is not referring to the other moment in another mistake where the same thing happens when they exit the boat. It actually happens twice during the scene - that moment and this one).