At the studio, Stacy has her gun out when they enter the room. It disappears when she is taken hostage, and then despite not picking it up she has it again after the foot chase.
Hooker, Corrigan, and Stacy are all at the scene for an extended time, and no detectives are present,. Patrol officers do not investigate homicides. This of course is a recurring error as it is a premise of the series.
In the studio, the suspect has Stacy in a classic hold- behind her with his arm around her neck and threatening her via a knife. When the suspect points the knife at Hooker and Corrigan, Hooker despite being only a couple of feet away does not take the head shot to save Stacy.