Plot hole: Jamie and his witness are in a patrol car when they are attacked by criminals in a van firing machine guns at them. Jamie (of course) chases them away after a prolonged firefight, and when the van is driving away we see another patrol car also shooting at the fleeing suspects. There didn't appear to be any cars with Jamie, nor did anyone come to his aid during the gunfight, and this other patrol car was facing the wrong direction.
Plot hole: Early in the show, Jamie is in a patrol car escorting a witness when they are attacked by several guys in a van. The side windows of their cruiser seem shatterproof and withstand many bullets, while the rear window is shattered immediately. NYPD cruisers do not have bulletproof windows.
Continuity mistake: After the accident, Baez has a scar on her left cheek. However, during the raid, the scar moves to her right cheek and back to her left cheek. (00:27:12 - 00:49:32)
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)
Other mistake: Danny, while driving home with his family, hits a man with his car. Danny gets out of the car to attend to the man, but his wife, Linda, who is a nurse, does not get out of the car to render aid to the man. (00:02:18)
Answer: The Seal of the City of New York.