Visible crew/equipment: As Danny gets out of the car, with the bad guy who shot Erin in the courtroom, holding her hostage and coming out to meet him behind the courthouse, as Danny gets out of the car, in the driver's side car door mirror you can see a crew member in a red shirt holding one of those "scene marker" slap boards. (00:32:40)
Continuity mistake: During the courtroom hostage scenes, when Raoul Delgado and Erin are on the phone with Danny there are some closeups of the gun Delgado is holding. After Delgado hangs up on Danny, when he slams the gun into Jack's temple and orders Erin to go with him, in these closeups the gun is noticeably different. (00:30:55)
Continuity mistake: After Danny shoots Delgado, he kneels down and holds Erin at her right side with his back facing the car (driver's door is open), but in the next shot Danny is kneeling at Erin's left side with his front now facing the car, as seen in the live feed Frank is watching on the monitor. The live feed is not backwards, note the open driver's door, etc. (00:34:35)
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.