Continuity mistake: The scene where Boyle explains the case for Scully and Hitchcock you can see the same two people walking by the room 3 times, coming from right to left in the background. (00:08:30 - 00:09:20)
Character mistake: Captain Holt calls the Pimento case "Operation 225641441636324" which he said he arrived by placing a numerical value to each letter in Pimento and then squaring it. But the perfect squares couldn't match up to Pimento since there's only 6 perfect squares and Pimento has 7 letters (plus the last 2 perfect squares don't fit the pattern of the previous 4). Nor is "225641441636324" a perfect square.
Continuity mistake: When Charles approaches Adrian about how much longer he's going to stay at his place, he knocks stuff off the desk leaving a pink folder. After Adrian takes the fork away from Charles' neck, there are now extra folders on top of the pink one.
Plot hole: Amy lets Scully place the watch in the break-room, but how could she have known that after Captain Holt steals the crown out of the locker, he would go there? And not, for example, go back through the window he came from.
Character mistake: When Charles is talking about Terry's kids you can see Stephanie Beatriz (Rosa) trying not to completely crack up next to him.
Character mistake: When Charles gets kidnapped Terry screams out Joe instead of Charles. (00:05:50)
Continuity mistake: When Jake is explaining why he let Richmond go, the left zip of his hoodie goes from folded out to flat between shots and back again a few times. This is especially noticeable when he says "the old me." (00:18:07)
Continuity mistake: The flyers on the top and bottom of the pile Terry is holding keep changing colors.
Continuity mistake: When Jake and Boyle talk about Jake's Dad, a man (grey clothing and holding a cup) in the background (behind Boyle on the left) walks from the back to the front in the same way in both shots. (01:45:00 - 01:55:00)
Continuity mistake: When Charles is talking to Gina in the break room while wearing the mask, he takes it off. When he says she was being sweet, it's back on.
Mr. Santiago - S4-E7
Revealing mistake: When Jake is typing on his computer just before Terry talks to him about meeting Amy's dad for the first time, his computer is and remains on the desktop doing nothing. (00:02:05)
Continuity mistake: When Jake handcuffs himself to Captain Holt, the cuffs around each of their wrists consists of double metal bars connected to a single bar. The direction of the handcuffs changes a few times, going round their wrists the opposite way, which is quite impossible. Then the same thing occurs when Boyle handcuffs himself to Holt. (00:09:35)
Continuity mistake: When the lights go off after attaching the belt to the ceiling, Holt is interrupted before he finishes the word "winner", however in the flashback he says "winner of the 5th annual-" before being interrupted.
Revealing mistake: In the opening credits (the very beginning), Jake is walking and the image behind him is blurred. When it unblurs (right before it the shot changes), the phone number on the building behind him is 213 which is LA, vs. 718 which is Brooklyn.
Character mistake: When Wunch frisks Holt in order to "check for a wire," she appears to forget that her actions are easily visible through the interrogation room's mirror, something a high ranking official in the NYPD would not likely forget. (00:11:41)
Other mistake: Holt takes the crown out of the back of Jake's cabinet. However this wouldn't be possible as the crown was in the top drawer. This would have a back on it and it wouldn't be accessible by just removing the back of the cabinet.
Other mistake: When Amy reaches down to get the key out of her shoe she literally only bends slightly. There is no way that she could've reached all the way down to her foot, or retrieve the key in the seconds before she gets it. (00:14:30)
Character mistake: Jake and Rosa are looking around in The Apartment for months. 14 CIS workers are analyzing The Apartment. All of them are looking for a killer who never left The Apartment. Still, in multiple months no-one thinks about checking the person-sized vents. Seems pretty unlikely. Vents are literally the first thing anybody thinks about when people try to disappear. And a vent of this size is a dead giveaway that someone for sure would have checked.
Revealing mistake: When the motor home explodes, the flames from the explosion are CGI. It doesn't look very realistic at all.
Continuity mistake: When Terry's wife Sharon walks into the station, she's wearing a purple dress. When she announces her water has broken while in the interrogation room, she's wearing the purple dress. After returning from commercial break, she's still sitting in the exact same spot but now wearing a burgundy tracksuit and lavender top. (Perhaps she changed clothes because her water broke however, it's highly unlikely since she is sitting in the same place and doesn't look like she's left the room).