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.
Factual error: The U.S. army would never intervene in a hostage situation on American soil. Legally they're never be deployed for any reason on U.S. soil unless invaded by a foreign military. The F.B.I, S.W.A.T, state and local police agencies could have easily dealt with the events at the school.