Episode #1.1 - S1-E1
Continuity mistake: Luther goes to see Zoe and the house is an end terrace with a red door. Later he goes back and it's mid terrace with a black door.
Suggested correction: No, I don't think this is an error. I think the house with the red door is Luther and Zoe's marital home and the house with the black door is Mark's home.
That's what I thought, but how did he know where Mark lived?
I think it's a mistake because Riply is outside keeping watch on Zoe's house. At that point, Luther didn't know who Mark was, so how could he know where he lives?
Episode #1.3 - S1-E3
Character mistake: Luther and Ripley pretend they have not been on the boat and did not find the victim's body as they do not have a search warrant and do not want to compromise the case. However, under English law a police officer may legally enter any premises without a warrant in order to save life, prevent injury or protect property. Since they have a reasonable belief that the victim is being held prisoner on the boat and her life is in danger (as far as they know at that time she is still alive), they don't need a warrant. As experienced police officers, they are bound to know this.
Episode #1.2 - S1-E2
Character mistake: A number of times the police officers refer to Owen and Terry Lynch as being soldiers and in the Army. They were in the Royal Marines, part of the Navy, and Marines are Marines, not soldiers.
Episode #1.2 - S1-E2
Character mistake: Owen refers to his own unit as Forty Six Commando. The Royal Marines pronounce the names of commandos as individual digits: Four Six Commando.
Episode #1.5 - S1-E5
Other mistake: Ian is pointing a gun at Luther in the hotel. The maid starts to open the door from an adjoining room (roughly 4 meters away). Ian starts firing at the door, and Luther falls over on the spot he is standing on. Half a second later, Luther is through the door pushing the maid to the floor. What about the hail of bullets he must have had to go through to get to the door? (00:47:00)
Episode #1.3 - S1-E3
Visible crew/equipment: During Luther's call to Alice, a boom microphone's wind protector briefly enters above his head before the scene cuts. (00:23:35)
Episode #1.3 - S1-E3
Factual error: The detectives determine that the killer must be using a boat which he used to dump the first body next to a canal in Birmingham. However, the barge he is using is far too large to navigate the Grand Union Canal from London to Birmingham, let alone the canals within Birmingham itself.
Episode #1.6 - S1-E6
Character mistake: DCS Cornish refers to "Detective Chief Superintendent Schenk." At that time he is a Detective Chief Inspector.
Episode #1.6 - S1-E6
Continuity mistake: During the fight with the shotgun Luther's hand is right at the end of the gun barrel. When the gun goes off and breaks the glass his hands are further down. (00:50:00)
Episode #1.6 - S1-E6
Continuity mistake: At Waterloo International station at the end of the episode, after Luther gets the shotgun off DCI Reed, in the ensuring conversation John Luther's collar on his coat goes from being up to down between shots. (00:51:00)
Episode #1.6 - S1-E6
Other mistake: A detective is watching footage on a computer screen of the standoff with Luther and Reed where police snipers are on rooftops. Someone walks across the screen right behind Luther and Reed. Surely the police would have cordoned off the area with the snipers on the rooftops.
Episode #1.5 - S1-E5
Continuity mistake: The position of Zoe's sweater on her right shoulder is constantly changing while Luther is holding her dead body near the end of the episode.