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.
Factual error: The ID cards for the chief petty officers all show them in junior rates' round hats and 'sailor suits'. CPOs (and petty officers) wear officer-style peaked caps and jackets and ties. It is unlikely that they've never had their photos changed since they were junior rates.
Factual error: None of the naval officers wear medal ribbons. Even if none of them have been in a war zone (unlikely) or received an honour (also unlikely, especially given one is an admiral), the more senior would still have jubilee medals and the long service medal.
Continuity mistake: Kirsten is referred to as a DC (Detective Constable) in the first half of the series and then as a DS (Detective Sergeant) in the second half. As these later episodes include flashbacks to before the previous episodes, she obviously hasn't suddenly been promoted.