(At around 1h 29 mins) There is no ferry route between Norway and UK. the now defunct route connecting Newcastle in England with Stavanger, Bergen, and Haugesund in Norway shut down in 2008. But there is plans to reopen a route in 2026.
Jamal's supposed arterial bleed is not very intense and should not have caused his death if well managed by applied pressure or doing a proper Combat Arterial Tourniquet, likely available in the SWAT team gear.
(at around 1h 29 mins) There are no Ferries that sail directly from the port of Dover to Norway. The closest you could get would be Denmark and drive the rest of the way. Whichever route was taken, it would take more than 24 hours.
(at around 16 mins) The plot involves a broadcast on 65.8 MHz but the broadcast FM band in the UK starts at 87 MHz so a 'normal' radio receiver could not tune to it.
In the Red Room, each subscriber had their own camera (evidenced by the red lights blinking off when they logged off. Whereas there would have been several cameras for different angles, the stream being broadcast would have been the same for all users.
There is no netting between floors of the prison. The netting prevents prisoners' from being harmed if thrown over the side and from any personal harm.
A henchman is on a phone call with the villain then turns his smartphone towards a TV or PC monitor to show captive women but this is not a video call, so pretty useless move.
Jamal's supposed arterial bleed is very poorly managed: heavy pressure should be put on his wound instead of trying to use a belt for a Combat Arterial Tourniquet.
Nearly at the end of the movie, Luther operates a smartphone whilst under water. This is not possible.
Towards the end after Luther is saved from the freezing cold Norwegian waters, he is understandably wrapped in a blanket presumably to prevent hypothermia. He then removes said blanket to reveal he's still in the same suit he was wearing whilst in the freezing water which would be soaking wet.
(at around 1h 55 mins) The helicopter returning an injured Luther to England from Norway manages to fly over the white cliffs of Dover, which are in the far south of the UK and would require an enormous and senseless detour.
They say they are taking the ferry to Norway, but EMTs are wearing Estonian uniforms.
The final is presumably taking place in Norway. The ambulance personnel visibly wear uniforms with "Tallinna Kiirabi" (Tallinn ambulance). Tallinn is the capital op Estonia, which is about 1000 kilometers away from any place in Norway...
The vehicles come faster and faster onto Piccadilly Circus and crash violently. A driver's first instinct is to brake, so there should be lots of cars bumping into each others but not at high speed as shown.
Abdominal wounds heal much faster than do wounds to the forehead.
Very poorly managed arrest of the villain by Jamal, supposedly a trained SWAT police person.