Factual error: Chief Superintendent Hilton wears the ribbons of the General Service Medal (awarded for military service in a combat zone, most commonly in Northern Ireland) and the Police Long Service and Good Conduct Medal (awarded for twenty years' service), but not the Golden Jubilee Medal (awarded to all officers with five years' service in 2002), which he would also have. When he reappears in Series 4, he is wearing the Golden Jubilee Medal, Diamond Jubilee Medal (awarded in 2012) and Police Long Service and Good Conduct Medal, which would all be correct, but no longer has the General Service Medal.
Plot hole: When Nicky goes into prison in Mexico to give a criminal a shot of insulin, two errors are seen. 1) The needle and syringe are far too big for an insulin shot, which takes a one ml syringe and a small sub-cutaneous needle. 2) When we first see the syringe, there is a small amount of insulin in it, but it grows the more times we see it, until a large syringe is two-thirds full - insulin is enough in a one ml syringe.
Continuity mistake: Kurt is still recovering from the beating he took in the previous episode with bad cuts on his forehead, checks and temple area. They are red and impossible to miss while he is in the police station. The cuts have miraculously disappeared in the next scene when he goes to visit Mona.
Continuity mistake: When Buzz and Provenza race out of the squad room to follow Rusty in the frantic search for Stroh, Buzz is in shirt sleeves with no tie. However when they arrive at their destination Buzz is wearing a coat and tie.
Visible crew/equipment: After Hutch finds the ticking box with the clown and Starsky's badge inside, when it cuts to Hutch and Dobey walking toward the squad room, the cameraman and camera are reflected on the door's glass window. (00:17:20)
Revealing mistake: When the thief places The Blue Carbuncle in the goose's throat, it's obvious he actually doesn't put the gem in the bird's mouth. He pretends to, but then drops the gem into his other hand. This is all visible in the shot.
Factual error: Noticed this watching season 2, and I assume it was also the case in season 1. The entrance of the Miramar Playa has flags from various countries flying. One of them is the Canadian flag with the maple leaf. Wrong flag. In that period the Canadian flag was the "Red Ensign", or "Dominion Flag." The maple leaf flag wasn't introduced until 1965.
Other mistake: When Cobb starts to chase the red Dodge, there's a shot of him passing between two vehicles (and very distinct buildings in the background). When Murphy picks up the chase, this same shot is reused, showing her passing between the same two vehicles.
What They Saw in Southie High - S1-E2
Other mistake: Agent Rohr asks who the cold case is related to. A dossier is given to him and the front cover contains a photograph and the name "Kanicki, K". Agent Rohr says "Kelly Kanicki" but there was no indication of the full name, just the initial. (00:08:30 - 00:09:00)
Triumvirate of Terror! - S3-E8
Continuity mistake: Lex busts through the glass doors in S.T.A.R. Laboratory and the glass falls to the ground. In the wide shot, it is yellow. But in the close up of Lex's feet, the glass is suddenly clear. There is also more of it in the close up. (00:05:35)
Borealis 301 - S1-E5
Continuity mistake: Near the end, Tom takes out the cipher key that was previously written on. But the cipher key used in the close up shots is different than the original. The words are spaced out and crossed out differently.
Death by Resurrection - S1-E12
Continuity mistake: McBride and Ryan are driving through town in heavy traffic. When the shot cuts (and their conversation continues uninterrupted), not only does the rear view mirror disappear, but an obvious rear screen projection changes their locale to a country road with trees and no traffic at all. (00:06:00)
The Secret Fate of All Life - S1-E5
Continuity mistake: The first time we see Detective Cohle being interviewed by the other two detectives, two of the beer cans on the table in front of him completely vanish between shots when he asks to see the rest of the discovery file.
Character mistake: When the bodyguards enter elevators, they always enter last; they should be entering first to ensure it is secure. This is particularly visible in the hotel where the elevator can stop on any floor and Special Protection Branch does not have complete control of it as an express.
The Two Deaths of Jamie B. - S2-E4
Revealing mistake: When Naomi shows Kirsten the money, you can tell it's fake. Not only are the serial numbers all the same, you can read "this note is not real it is to be used for motion pictures."
El traje del tío Jacinto - S2-E16
Visible crew/equipment: In the credits, there's a unknown person hiding behind Don Ramón (Raymond).
The Blessing of Many Fractures - S1-E8
Continuity mistake: During the fight with Zhou Cheng, Cheng does a forward flip and kicks Danny, making him stumble backwards. In the shot of Cheng lying on the ground, Danny is holding his stomach. In the shot immediately afterwards, he's holding his chest.
Factual error: As Bentley is shown round the control room of the plant there are modern LED light panels and modern health and safety stop buttons which would not have existed in the 1960s.
Continuity mistake: In S:1 Ep.10 Maddie says she'll be 15 in a week. Season 2 picks up 6 months later. In S2ep5 Bosch uses Maddie's birthday to access a computer. Password is 01/10/01. This makes the date sometime in July of 2016. Then in S2ep6 George Irving is killed, and the end of watch broadcast lists his date of death as 7/24/2015. This error is reinforced in S2ep10 when they show a plaque being mounted to honor George.