After Lucas shoots one of the hostage takers, a SWAT team member checks for a pulse in his neck using his thumb to see if he is dead. A pulse is never checked with a thumb as you can feel your own pulse by doing so, giving a false impression there is a heart beat when there isn't one present.
During the hostage scene in the gym, the cell phone they are talking on is upside down in many shots.
As the guy with the weapon puts the cellular, an iPhone 4 maybe, to the ear of the teacher, the phone is wrong turned (the dock connector is up, camera and headphone down to the mouth)