Episode One - S1-E1
Factual error: In the fairground chase the characters jump over some Heras fencing that wasn't invented until the next decade.
Continuity mistake: When the hostages try to get some rubble to catch fire, they find that everything is covered in some flame retardant stuff. Yet, in the very first episode one of the very first things they do is to make a small fire to get the fire alarm going.
Factual error: When Tom is locked up in an institution for the mentally ill, he is given a bed on a mixed gender ward/wing (both men and women). Wings and wards in mental institutions have not been mixed gender for more than 100 years - it is inconceivable that this practice would be existing in the 1990s in a large city in the USA.
Factual error: Thomas holds the Gendarmerie rank of Capitaine (by which he is frequently addressed by his subordinates), and thus should wear three horizontal silver bars on his epaulettes. However, in the only scene where his rank is displayed he instead wears the two chevrons of an ordinary gendarme.
Factual error: Possibly a mistake from the novel on which the series is based, but although he later became Bishop of Hereford, St Thomas Cantilupe wasn't baptised in Herefordshire. He came from Buckinghamshire.
Continuity mistake: Throughout the series, the Barbers pull their cars straight up their driveway. But the cars are nearly always shown coming back down the driveway driving forward.
Continuity mistake: When Mary talks to Bobby D at the crime scene, her hair moves back and forth over her left shoulder between shots throughout their conversation.
Factual error: The DI refers to the local policeman as "Officer" Fuller. No British police officer would use this term to refer to another British police officer. She'd have said Constable Fuller or PC Fuller.
Royal Jelly - S2-E1
Plot hole: It's all very well for Albert to humm "bzz-bzz" to indicate that he has been eating too much Royal Jelly and is no longer entirely human. But "bzz" is just the noise of bees flying, it's not a sound that they deliberately produce. It makes no sense to SAY "bzz." Suppose he was turning into a horse instead, then he might say "Whinny!", but he wouldn't say "Clip clop clip clop."
Factual error: In Massachusetts, Atticus, Leti and George are attacked by the local sheriff and his deputies, who are patrolling the county roads. In Massachusetts, sheriffs run the county jails, but they do not (and did not) handle routine policing, which is the responsibility only of municipal police departments.
Other mistake: Agent Maddy is approaching the scene of a downtown explosion and fire. She has her FBI badge showing on her belt. As she approaches the police line she rummages in her jacket and looks down at where the badge is, but reaches into the adjacent pocket to pull out another badge in a wallet. Why not identify herself with the badge on her belt?
Factual error: Constantine's driving licence is shown - it's a UK licence, but no. 7 where his signature should be is blank, and no. 8 where his full address should be simply says "England, United Kingdom." Both are printed onto the licence when it's issued - without that info it would never be issued in the first place. And it's not a fake, because why would he have a fake licence with his real information on it? It's just an incomplete prop.
Factual error: The FBI agent introduces himself and says "Mike Weston - I did my thesis on Joe Carol at the academy." FBI agents are required to have a university degree, but they don't write thesis' at the academy. A person is either in a university or at Quantico getting trained. They are not writing papers at Quantico. They need the degree beforehand to get in. (00:10:30 - 00:11:30)
Continuity mistake: As Rick is getting informed about the CRM's future plans, he is holding his knife under the table. The next shot shows his hand on the table, before showing his hand holding the knife under the table again. (00:23:50)
Angel of Mercy: Part Two - S1-E4
Character mistake: When Lenore Osgood is speaking on the phone with Charles Wainwright about killing Dr. Hanover, she mispronounces "Larynx" as "Lar-nix."
Factual error: DI Renton is a Metropolitan Police officer 'parachuted' into Kent to solve a big case. This hasn't happened for many decades. Local police forces investigate their own crimes without help from the Met.
Other mistake: Vincent falls from a parking garage and smashes onto the roof of his car, appearing nearly dead. In the next episode, he is in the hospital with multiple broken ribs and other fractures, yet he is released without even staying the night for observation.
Factual error: When Detective Inspector Sara Lunt's photograph in uniform is shown on the TV news she is wearing a double row of silver lace below her hat badge. Only chief constables wear this insignia, well above the rank of inspector.
Factual error: Jake and Miyamoto go to an establishment where there are girls dancing on stage. The girls are first dancing to "Motivation" by Kelly Rowland, released in 2011, and "Aly Walk With Me" by The Raveonettes, released in 2007. But, this scene takes place in 1999.
Factual error: Abby gets out of the train via the driver's door. You see a front view of the train. The number on the train is 321434. This train runs on overhead lines, and it is being shown as a Gatwick Express train from Gatwick Airport to Victoria. The railway from Gatwick to Victoria has a third rail conductor, so this Class 321 train would not have been able to move. (00:50:02)