In and Out - S7-E14
Continuity mistake: At the start, the rearview mirror on the windshield of Eddie and Jamie's squad car disappears and reappears.
Continuity mistake: When Danny and Jimmy drive up to D'Angelo, the rearview mirror appears, disappears, and reappears on the windshield (though its small square adhesive is intact). (00:28:30)
Continuity mistake: As the couple with their two children are walking down the street, the daughter, Sophie, is holding latex helium balloons which are the transparent type, but after she and her mother are struck by the reckless drunk driver, when the balloons float away they are the opaque type. (00:04:25)
Continuity mistake: Part way into the episode they show the front of Jamie's Ford police car and the car number on the front plate, but when they pull up to the court house to talk to his sister, it's a Chevrolet police car with a different number on the front. (00:09:05 - 00:09:40)
Confessions - S7-E9
Continuity mistake: We can see Jamie driving a Ford CVPI with plates reading 7554, however when he appears in the following shot in the court, where he was going to in the previous scene, he's driving a Chevy Impala with plates 61795. I am not sure, but I think this error happened in the previous seasons as well. (00:09:08 - 00:09:48)
Continuity mistake: Franks makes a comment that there have only been 18 deaths last year in New York, but Danny on his own closed more than 30 in the season before.
Continuity mistake: When Danny/ Baez and Jamie go to arrest the medic, there are a few different shots where there is snow on the ground and then none, likewise no snow on cars and then a lot. (00:08:00)
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.