Officer Down - S1-E4
Factual error: Danny and Jackie Curatola are with ESU to make an arrest at a garage. They are behind cover with their weapons drawn. Although there is no suspect shooting at them, both Danny and Jackie have their fingers on the trigger, which is against police training unless you are going to engage a subject by shooting your weapon. The ESU officer right next to them does not have his finger on the trigger. (00:38:04)
Dedication - S1-E15
Factual error: When the ambulance pulls up to the hospital after Frank is shot, it is a Chicago Fire Department ambulance, not New York. (00:02:10)
Answer: It's a common cop show plot device. If the police on the show always acted in the most logical way (i.e. not alerting a suspect to their presence) the show wouldn't have the opportunity for an exciting foot chase.