Factual error: Wanda's father opens his briefcase of DVDs and one of them is Malcolm in the Middle. But the bomb that killed him fell in 1999, and Malcolm in the Middle didn't start airing until 2000.
Factual error: As the Royal Navy has its own police (including detectives), there would be no need for a civilian detective to be airlifted onto a submarine, especially to investigate a sudden death that was not originally believed to be a murder.
Suggested correction: The Royal Navy police are not equipped to handle murder; local police are usually used for more serious offences so no claim of a cover up. There are no MoD police attached to a submarine either, so in theory somebody would have to go to the boat. (However they still wouldn't risk surfacing).
Initially there is no suspicion of murder, only an unexplained sudden death. There would be absolutely no need to airlift a civilian detective aboard a top-secret submarine. It wouldn't be the first time a sudden death had occurred aboard a Royal Navy vessel.
The Crossing - S1-E4
Factual error: The Dutton camp as well as Shea Brennon and Thomas are using modern thin Teflon/non-stick coated coffee mugs/pot.
Power Broker - S1-E3
Factual error: Every guard in the prison has the emblems of Hamburg on his/her shoulders of the uniforms. Zemo is said to be imprisoned in Berlin, so they are wearing the wrong emblems.
Factual error: Bessie says she was going to study veterinary medicine at Texas A and M. That would have been approximately 1940. Neither women nor people of colour were admitted to TAMU until 1963 so she could not have even been able to apply.
Factual error: The Chief Constable of Dyfed-Powys Police is depicted as a mixed-race woman named Tyler. At the time, the chief constable was actually Terry Grange, a white man. The only woman to ever head the force, temporarily in 2012 (after the period covered by the series), was Jackie Roberts, who is also white. This is a factual series covering real events, not a work of fiction.
Family Day - S2-E5
Factual error: The phone number Harry is given has an exchange that starts with "0" (the first 3 digits after the area code). Phone numbers (in the US) can't start with "0" since that's the "operator."
Factual error: When Alina stands outside of the door to the banquet hall, waiting to demonstrate her power to the king and queen, there is a modern electronic occupancy sensor on the wall behind her.
Factual error: Season 2, Episode 1: Cleon is fighting some "ninja" warriors. One of them slices part of an android's head clean off, below the right eye. When the android is next seen - with part of its head cut off - the slice is above the right eye. The right eye is fine.
Factual error: A passerby tells Sheldon Sampson that the stock market has just gone "tits up." This is a British expression that you would likely not hear in the United States, and you certainly wouldn't hear it in the 1920's.