The City That Never Sleeps - S4-E2
Continuity mistake: Danny and his partner are driving with a passenger in the back seat. You can see both front seat headrests removed while they are talking in the car. Next shot shows the car from outside and you can see the headrests are on the seats.
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)
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: 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)
Continuity mistake: Danny and Linda are hugging after Danny tells the boys to go pay your respects to the WWII Memorial. In the next shot they are standing apart as when he told them to go pay their respects to the memorial. (00:54:34)
Continuity mistake: Near The End of the episode, just after Danny's family is looking at the Statue of Liberty, Danny puts his arm around Linda, and then does it a second time.
Other mistake: Danny says "14 years ago today I kissed Linda" but in previous episodes they were celebrating their 16th anniversary.
Continuity mistake: When Frank goes to see Gallo at the hospital after the lawyer's arraignment, Frank drops a deck of cards on the bedside table beside the bottle of whiskey, but the bottle has vanished in the next shot. (00:41:00)
Continuity mistake: One second Frank Reagan throws his glasses on his desk, the next after a brief cutaway, they are on his face. (00:36:10)
Other mistake: Throughout the episode, all the interactions with the characters went from day to night except for Commissioner Reagan chaperoning his grandson's class at the museum. It stayed daylight the whole time at the museum. (00:27:14)
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)
Continuity mistake: In the first two shots of the family dinner Henry is holding his fork up in his left hand, but in the third shot from behind him (facing the family) his raised left hand is empty with his fork lying across the plate, then it's back up in his hand in the fourth shot. (00:21:10)
Continuity mistake: During the family dinner, while everyone discusses the use of body cameras Frank is wearing his eyeglasses, but in the shots facing Linda during the conversation Frank's eyeglasses are gone. (00:21:40)
Character mistake: Frank implies that Joe is the oldest child, but he was born in 1977 (1x22), Erin in 1975 (6x07), and Danny 1973 (2x17). Erin also claims she wasn't born yet when the murder of Henry's friend took place in 1977 but she would have been about two years old.
Character mistake: Sergeant Gormley is promoted to Lieutenant in the previous episode. In this episode he is referred to as Sergeant Gormley by Commissioner Reagan and Deputy Commissioner Garrett Moore at least twice.
Character mistake: In this episode, Garrett says that "Nom de Guere" means pen name. It means war name. Nom de Plume means pen name and Garrett is supposed to be an expert in his field.
Continuity mistake: Henry sets down the pencil he was using on the crossword. In the next shot, as he is picking up his glass, it is in between his fingers. It shows him taking it from his hand with the other, but again in the next shot, is back on the crossword. (00:40:30)
Character mistake: Throughout the episode they refer to the victim owning a "cement" company. In fact it was a concrete company. Although the terms cement and concrete often are used interchangeably, cement is actually an ingredient of concrete. Concrete is basically a mixture of aggregates and paste. The aggregates are sand and gravel or crushed stone; the paste is water and portland cement. (00:00:05 - 00:35:50)
Continuity mistake: Near The End of the episode Frank Reagan pulls up to the house of the woman who has been scamming New Yorkers with the fake 911 charity. Immediately before he arrives she is putting suitcases in the trunk of her car. As he pulls up the suitcases in the trunk are different.
Through the Looking Glass - S5-E19
Other mistake: Danny supposedly handcuffs an at-risk teenager. When the police officer takes her away to a cell, the girl isn't handcuffed. The handcuffs are just in her hands behind her back. (00:52:00)
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.