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)
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.