Continuity mistake: Frank is talking to Garret in his office. A close up shot shows him sitting at his desk with his elbows on it. A wider angle shot shows him sitting up straight. Next shot shows him with his elbows on the desk again.
Continuity mistake: Frank and Henry are up late, 3am, and, talking about how his late wife Mary never wanted to see her youngest go into the Family Business. Henry says how proud Mary was in the day of Jamie's graduation. But Mary was already dead by the pilot, when Jamie graduated.

Continuity mistake: The Reagan men sit at the table for a drink. Jamie's glass moves towards/away from him in different shots. (00:23:15)
Dedication - S1-E15
Revealing mistake: Frank gives Walter a new cigar. However, in the closeup when Walter puts the cigar in his mouth The End of the cigar is burnt and shows that it was once lit and put out. (00:01:35)
Continuity mistake: Jenko and Witten confront a guy creating a commotion in a market. The felon runs past them out to the sidewalk where, somehow, the two cops are waiting and grab him.
Fog of War - S10-E14
Factual error: During the funeral towards the end of the episode, both Jamie and Eddie are wearing white shirts with their dress uniforms. In the NYPD, only Lieutenant and above wear white shirts, like the show has portrayed. The color doesn't change for the dress uniform. (00:38:35 - 00:41:14)
Continuity mistake: Toward the end of the episode when the older mobster is walking from his car down a narrow alleyway toward home, he passes under a low hanging outdoor light fixture. When he is accosted by the other mobster with a gun they are standing with the light fixture between them. There is no movement, but when the police arrive, the light fixture is well behind the guy with the gun.

Visible crew/equipment: When Eddie and Jamie stop to help the woman holding the boy, in the exterior shot as Jamie gets into the back of the RMP with the young boy, the reflection of camera equipment is visible on the window. (00:04:55)

Continuity mistake: While Danny and Baez are questioning Damian about Mason's whereabouts, Damian's right handcuff switches to the opposite way depending on the angle of the shots. Either the single metal bar faces up or the double bar faces up, which is quite impossible to change when it's locked around his wrist.

Visible crew/equipment: After Anthony drives the Porsche 911 into the garage, in the shot facing Erin and Anthony just as Jimmy gets into the car, the green T-mark, the red tape mark, and blue tape mark are visible on the floor.
Visible crew/equipment: After Danny and Baez get the hospital physician's rundown on Joe's condition, when the partners reintroduce themselves to Joe the reflection of the boom pole/mic is visible on the glass behind Danny.
Visible crew/equipment: When Eddie comments that the Rough Tough Cream Puff made a collar, she and Jamie walk up the hallway, and before Eddie reaches the doorway we can see the red tape mark on the floor as we hear Marcus brag, "mad fast." (00:15:55)
Visible crew/equipment: After Frank tells Garrett to set up the meeting with Thomas and agrees to play nice, when it cuts to Erin as she walks toward Zach and the AG, the T-mark and white tape mark are visible on the floor in front of the two men. (00:01:50)
Fresh Start - S6-E15
Continuity mistake: When Erin is in the ladies' room walking toward the door, she finds Anthony "lurking" in the hall, and Erin's eyeglasses which are hanging from her crew-neck top go from facing her right side, to her left side, then back to her right side, between shots. (00:31:55)
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.
Other mistake: Danny says "14 years ago today I kissed Linda" but in previous episodes they were celebrating their 16th anniversary.
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)
Visible crew/equipment: Towards the end of the episode as ADA Reagan is walking to her car, you can see the cones in the DAR end of the street the filming crews used for traffic control to keep traffic off the set. (00:02:30)
Character mistake: Commissioner Frank Reagan refers to Lt. Gormley as Sgt. Gormley in this episode. (00:08:30)
Continuity mistake: As Danny and Jaime are at the range shooting near the middle of the episode, their targets from behind and the grouping of shots they take are really tight together. When they retrieve their targets a minute later, the grouping from the front is completely different and further apart than what was seen from behind the target.
Answer: It's the New York Police Department flag, created in 1919. The stripes represent the 5 boroughs and the stars the different towns that made up New York (including New York City itself).
Bishop73
What about the other flag that is not the U.S. flag?
Please be more specific. Are you talking about the New York City flag?
Bishop73
It is the Iowa State flag. At least in the episode from 1/22/21.
It wouldn't be the Iowa State flag. Plus the Iowa State flag is blue, white, and red. The flag I think they're talking about is blue, white, and orange.
Bishop73