They couldn't have monitored or guarded every inch of the school's walls - that kind of security lapse happens everywhere, no point beating ourselves over it. We need to take steps, maybe assign a squad of Police Elite Force / Rangers / FC to patrol each school instead of licking politicians' feet.
I believe the Army was talking about tracing the uniforms they used, that would be a good step.
More importantly, we need to improve the NACTA system to ensure better early-warning and counter insurgency.
They didn't round up the teachers, according to Gen.Asim Bajwa they entered classrooms and killed everyone there. Teacher was most likely in the class, it's possible they were searching for her but they definitely killed everyone else in every classroom they could find.