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
Continuity mistake: At the start, Frank isn't wearing glasses at the table. Then in one shot he is. Then not again. (00:00:40)
Dedication - S1-E15
Revealing mistake: Frank gives Walter a new cigar. However, in the closeup when Walter puts the cigar in his mouth The End of the cigar is burnt and shows that it was once lit and put out. (00:01:35)
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)
Dedication - S1-E15
Continuity mistake: When Danny gets into gunfight with Rory Brennan at Whitey's facility, keep a good eye on Rory's gun. After Danny shoots him, the gun drops out of his hand onto the ground between his legs. When Danny goes down the staircase, the gun is back in Brennan's hand, so Danny uses his foot to bring the gun to the floor...for the 2nd time. (00:29:50 - 00:30:35)
Revealing mistake: A runway model drops dead. Linda runs over and checks her. The model blinks, and Linda announces she is dead. (00:06:20)
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.