Palimpsest - S1-E6
Other mistake: During the credits, it lists Gloria Mundy as the actress who played Alison Araya. However, Araya is the actress's real name and Mundy is the character's name.
The King of the Delta Blues - S2-E6
Character mistake: "Are you going to send in the calvary?" is said twice. It should be "cavalry". (00:09:40)
Continuity mistake: When Dmitri and the doctor first try to get Vanessa to feed on human blood, the blood bag keeps switching from full to half-empty from one shot to the next. (00:16:05)
Factual error: A 3 series BMW from either 1979, 1980, or 1981 shows up in 1973 New York city. (00:32:15)
Other mistake: Issac is on the phone with his boss and he is holding his phone upside down, noticeable because his otter box case is upside down. (00:14:41)
Factual error: The judge requires £100,000 to be paid to the court in bail and Yvonne's husband later says he had to cash in bonds to get the money. In Britain, bail is not paid in advance. It is sufficient to prove that it is available if necessary and it is only required to be paid if the defendant later absconds.
Continuity mistake: When Will tackles Andrew, his shirt is lifted up exposing a blue undershirt that's tucked in, which is also behind his gun. There's two shots of this, but in the next shot, right before Will punches Andrew, we don't see the undershirt.
Continuity mistake: Harry drives away from a crime scene and his rear numberplate is visible as D703 VAN. We then see Harry in his car from the front, and the numberplate has changed to E160 HLT. (00:21:18 - 00:22:31)
Factual error: Pierre Bezukhov's spectacles are of the type with nose pads, which were not invented until the late 1920's.
Factual error: The story is set in the 1850s, but when Greshambury Manor is shown at night, it is obvious that the front of the building is illuminated by electric lights.
Factual error: You can see the Unicredit Tower on the Milan skyline - the episode should be set in 1997 but the unicredit tower was built in 2012. (00:31:00)
Factual error: Cars in Thailand drive on the left side of the road with the steering wheel on the right, unlike the ones shown in the episode.
Factual error: The Metropolitan Police isn't a national police force (except for close protection and anti-terrorist matters). It has no authority over other police forces. It doesn't take over criminal cases from other police forces. It hasn't even provided investigation teams on request for decades. Every force handles its own investigations. A Met chief superintendent and his team coming in, as depicted here, and taking over an Avon and Somerset investigation just wouldn't happen.
Episode #1.2 - S1-E2
Factual error: The railway tickets just say "Kent to Greenwich" instead of specifying the actual station where they were bought as they would have done.
Revealing mistake: As Sgt. Cain and Chief Lain stand by Marjorie's dead body lying on the hotel bed, discussing her death from an overdose, you can see her stomach rise and fall slightly, though she's supposed to be dead. (00:18:00 - 00:20:00)
Visible crew/equipment: While Michael sits outside of a hospital room in the hallway, there is a clear reflection of equipment in front of him. (00:21:00)
Continuity mistake: When Foster and his goons are at Asa's place and Asa is walking towards the door, he has already thrown the stick that he was fiddling with his toenails with down, and has both hands in his pockets. Shortly afterwards he has the stick back in his hand at the door.
Factual error: Almost all the people being shown skydiving have no experience doing it, but the instructor allows them to jump out of the plane unassisted after only giving a theoretic introduction into the subject. First time skydivers are always assisted in some fashion, usually through a tandem-jump or a parachute opened by a line attached to the plane.
Episode #1.4 - S1-E4
Other mistake: A major plot point is the rivalry between the Wehrmacht and the SS, who refuse to work together. After the explosion at the cemetery, it is the Wehrmacht who are explicitly described as rounding up and interning suspected resistance fighters, with the SS not being party to it. However, when Archer visits the internment camp, most of the staff are wearing SS uniform.
Factual error: At the picnic, a woman says she is going to New York by train. It is 1828. Railway passenger service in the United States did not begin until 1830 and it would not be possible to travel from North Carolina to New York until some years after that.