Continuity mistake: When Luis Cali is strapping Billy Tepper in the office, he is standing in front of the desk, while Billy is standing on the opposite side. Billy is facing him (while bending forward), so the strapping marks on Billy's back should be vertical, from head to butt, or at least diagonal. But later when the guys are cleaning the wounds, the marks are horizontal.
Continuity mistake: When the lead terrorist wakes up the morning after his father is murdered in prison, he discovers that the power has been cut to the school. Shortly after that, when the boys enter the restroom, you can see that the lights above the mirror and on the ceiling are lit. It may be possible for SOME lights to be working on battery power (like the ones above the mirror), but it's not likely that all of them would be battery backed up.
Continuity mistake: When the school is standing on the lawn after putting the professor's office there Sean Austin has a banana peel in his hand, in the next shot it is gone, and then it is back again.
Continuity mistake: When the military movies in to take back the school there is a wide shot of two helicopters on the ground with soldiers running out of them, the next shot shows many of those soldiers approaching the outer wall of the school ready to scale the wall with ladders. When the film goes back to the wide shot of the helicopters none of the soldiers or the ladders they were using can be seen against the wall.