Episode #3.2 - S3-E2
Factual error: The navigation software "What3Words" is featured. Apparently the words "flop, sponge, knee" point to a storage facility in London. In reality, they actually point to somewhere near the city of McGrath, Alaska. "Hunch, bumpy, strut" are also mentioned, which actually point to somewhere near Paraburdoo, a town in Western Australia, definitely not a forest in London as depicted in the episode.
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.
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.
Episode #1.1 - S1-E1
Continuity mistake: When Mark got into his cell, the top bunk had a vinyl-like covered mattress (or folded gym mat) that had a lengthwise seam along the middle of the side. He was not fixing his bunk bed while he was talking to cellmate Bernard, but when he was removing items from his bag on top of the bunk bed, it was now covered with a blue blanket and a sheet folded down by the pillow could be seen. A little later, the blanket was also covering the foot of the bed. (00:13:15 - 00:15:03)
Continuity mistake: When Chrissy and Lois are in the car before going into the meeting, the passenger side window is down, but not all the way. But in the next shot when Chrissy steps out, it's all the way down.
Other mistake: Danny Stevens, an undercover police officer, is killed. The police agree to investigate the murder of his undercover persona, Steve Daniels, thus allowing the investigation of his death without compromising their ongoing investigation into the activities of a drug kingpin. The officer investigating the murder visits the kingpin to ask about Steve's murder. She shows him a photo of the murdered man, but the name across the bottom is Danny Stevens - the policeman's real name.
Continuity mistake: When Carrie is about to leave the radio station, she's starting to put her left glove in. A shot later when she turns around it's already in.