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: 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: 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).