Visible crew/equipment: At the hospital, after Maria tells Danny about the busboy who was arrested for the same venue and same MO, it then cuts to Jaime undercover in the store. While Jaime walks toward Marco, the dealer at the counter, the camera moves at the same pace as Jaime, and we can see the reflection of the camera on the glass (between Jaime and the camera). (00:28:20)
Continuity mistake: When Danny and Baez confront Carmine to clear a few things up, Carmine tells them to call his lawyer. Just as Carmine clicks his key fob and his car explodes, Carmine's coat is entirely unbuttoned, but when he's blown backwards and slams onto the ground, in the first overhead shot of Carmine lying on the ground, his coat is buttoned up. (00:24:20)
Continuity mistake: While Danny and Waylon Gates are with Rodriguez at the safe house, showing him the photograph of his daughters, during this scene there is no picture hanging on the wall beside the door, but as they lead Rodriguez out in the last shot of the scene, a picture suddenly appears on that wall. (00:37:30 - 00:39:20)
Visible crew/equipment: At the safe house, while Danny and Waylon are alone with Rodriguez they "convince" him to call off his men, and in the last shot of this scene as they head out the door, the reflection of a crew member (presumably the camera operator) becomes visible on the picture hanging beside the door. (00:39:20)
Character mistake: Eddie is confronted by Captain McNichols after being caught in her office. Eddie responds by calling her Sarge, which is an incorrect title remark referring to a Captain. (00:38:46)
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.