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.
Episode #1.4 - S1-E4
Continuity mistake: The captain of the submarine has the rank of Commander (3 solid stripes) and half-way through episode 4 the captain suddenly has the rank of Captain (4 solid stripes) as shown on his shoulder epaulettes.
Continuity mistake: The captain (who holds the rank of commander) is in some scenes wearing four rank rings instead of the correct three he wears for the rest of the series.