Visible crew/equipment: After Anthony drives the Porsche 911 into the garage, in the shot facing Erin and Anthony just as Jimmy gets into the car, the green T-mark, the red tape mark, and blue tape mark are visible on the floor.
Continuity mistake: While Danny and Baez are questioning Damian about Mason's whereabouts, Damian's right handcuff switches to the opposite way depending on the angle of the shots. Either the single metal bar faces up or the double bar faces up, which is quite impossible to change when it's locked around his wrist.
Other mistake: Jamie races to the patrol car after witnessing a car jacking with possible child inside. He flings the door open, gets halfway inside, and the car starts without him even being close to turning the key in the ignition. (00:04:00)
Other mistake: Jamie and Eddie respond to a carjacking of a minivan. They are across the street and Eddie claims there's a baby seat in the car. There's no possible way that she could see if a baby seat was in the car. The minivan had dark tinted windows and only the driver's door was open. (00:05:00)
Factual error: Danny shoots Frank's revolver, and as he continues to shoot, you hear the sound of a casing hitting the floor, which shouldn't happen since it's a revolver being fired. (00:11:46)
Audio problem: While at the range, Jamie takes Frank's revolver to the line and fires it. The last 2 shots you can hear the casings hitting the ground, but not on the first 3 shots. The last 2 shots are from another camera angle. Revolvers don't eject the casings, so we shouldn't hear them landing.
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.