Episode #1.6 - S1-E6
Continuity mistake: The district commander wears the rank insignia of a chief superintendent up until the final episode, when he suddenly appears with the insignia of the lower rank of superintendent.
Episode #1.5 - S1-E5
Continuity mistake: The police force in the series is consistently described as the Yorkshire Police, a fictional force (and its name and crest are shown numerous times). However, when the detective superintendent is being interviewed on TV, the on-screen caption says he is from the West Yorkshire Police, the real force that covers the area.
Episode #1.2 - S1-E2
Continuity mistake: Sarah Lancashire has an eye injury. On visiting her ex-husband the scarring is gone. When she gets up it's back again. (00:50:40)