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.
Factual error: Superintendent Kane wears the insignia and uniform only worn by the Commissioner of the Metropolitan Police, not only six ranks above the rank he is supposed to be, but in an entirely different police force.
Factual error: At the end of episode 6, we see Alain crossing the German French border in a European registered right-hand drive Citroen CX. Then at the very beginning of Episode 7, they check into a hotel and the Mercedes parked in the forecourt was also right-hand drive. (00:01:00 - 00:01:30)
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: 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.