Other mistake: Murphy lands the helicopter on a railway line so an oncoming train will destroy it completely, and this happens exactly on cue with huge, dramatic explosions and flying debris. Apparently the train driver doesn't think this is important enough to interrupt his busy schedule - he doesn't stop the train. We do not hear brakes being applied - the wheels would make a noise like the sky coming down - and the train doesn't slow down at all - it just keeps on going.
Visible crew/equipment: At one point Clint Eastwood is out in the woods practising his shooting with his new .44 auto-mag pistol. While he's doing this, a car pulls up and a black male begins to get out with a shotgun. (We later learn that this is his partner). As the man with the shotgun is opening his door, if you look at the reflection in the car window, you can clearly see the reflection of a man with a camera and another man standing next to him.
Continuity mistake: In the first scene of their "training" for the big mission, the text "Somewhere near Galveston, TX" shows up as a subtitle on the screen. As it does this, there is a nice, dark aerial shot of mountainous terrain which is supposedly to hide the troops from any outsiders. The problem is, there are no mountains within hundreds of miles of the Island of Galveston. The whole terrain in this area is so flat that you can practically see from one side of the island to the other. (00:21:45)
Other mistake: In the scene where Jesse enters Monica's apartment, he consults her calendar to see in which class she is in school that day. There's nothing unusual about this until you look closely at the calendar and see that time time is early/mid August. Did her school's academic year run differently from other schools' years, or was she taking summer classes? The latter doesn't seem likely.
Visible crew/equipment: In the final fight scene on the cliff when they begin to battle in the air, you can see the wire pulleys on the right corner of the screen. (01:18:20)
Factual error: Star shuriken, despite common misconception, are not inherently deadly weapons. They were mostly used for distraction, since their lack of a single weighted point makes their attack rather inefficient (although the weapon could be coated with poison). Although it is possible to hit an eye, it is very difficult to hit such a small target or scoring a sufficiently deep wound to penetrate to the brain with a star shuriken.
Factual error: The caption says "twenty years later" before the main part of the movie starts. Now judging by the dates we've seen on-screen so far that would be in the reign of William and Mary, not Queen Anne.
Other mistake: During the scene in which Jackie and his girlfriend are being chased on bikes they hide in a shop. When the men chasing them stop outside of the shop, the subtitles read 'This is a dead end, we'll spilt up'. Spilt up?