Factual error: The series is based in the east-facing Deal, Kent. Even if this is not explicitly mentioned, there are visual references to the Thanet and Dover Police. So how can you have repeated sea view sunsets? Either that or they are having wine for breakfast at the breakfast table. The sun rises in the east and Deal enjoys a beautiful sunrise.
Factual error: Everyone, including other police officers, addresses the detectives as "Detective" rather than using their ranks of "Inspector" or "Sergeant" as they actually would.
Factual error: DI Renton is a Metropolitan Police officer 'parachuted' into Kent to solve a big case. This hasn't happened for many decades. Local police forces investigate their own crimes without help from the Met.
Episode #2.3 - S2-E3
Character mistake: DS Maxwell comes to Katy's house to interview her but when he introduces himself he says "DI" Maxwell.
Episode #2.6 - S2-E6
Plot hole: Laura is spotted at an airport where it is assumed she goes to Edinburgh. Although she mentioned later on she broke her bail by leaving the 30-mile radius by her bail conditions. This wouldn't have been possible as part of her bail was to surrender her passport.