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 #1.3 - 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 #1.6 - S1-E6
Character mistake: DCS Cornish refers to "Detective Chief Superintendent Schenk." At that time he is a Detective Chief Inspector.