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 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.
Other mistake: When the police first arrive at the school, one of the terrorists appears to fire a .50 caliber machine gun at the front of the squad car, causing minimal damage. If that were true, the entire car would have been torn to shreads. I was in the US Army, and have fired the M2 .50 caliber machine gun. The rounds for one of these are big and heavy; they can shoot down aircraft, or destroy armor plated vehicles.
Visible crew/equipment: In the scene where the character played by Sean Astin sneaks out of the school compound, after he goes out the window he dashes behind a car. A ferny pad is visible in the shot. A ferny pad is a blue fire resistant blanket that comes in handy on set and was probably placed there to keep the actor off the bare ground.
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.
Visible crew/equipment: During one of the final shots, the camera is panning around the main characters as they acknowledge Sean Austin's character and are celebrating. Two times during this shot, the camera shadow is visible on the bottom of the screen as is the head of it's operator.