(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, which would likely be available in the police team's equipment.
(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 were 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 has 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.
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.
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.
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.
Nearly at the end of the movie, Luther operates a smartphone whilst under water. This is not possible.
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.
(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 finale is meant to take place in Norway. The ambulance personnel visibly wear uniforms with "Tallinna Kiirabi" (Tallinn ambulance). Tallinn is the capital of Estonia, which is about 1000 kilometres away from Norway.
The snowy area that the Dover ferry takes them to, ostensibly in Sweden, has way too much snow to be that close to London which showed no snowy weather. The astute observer will note the layers of lava in the surrounding mountains places the filming in Iceland. And those lakes with frozen bodies would melt during the summer, spoiling the reported 7-year deep freeze.
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.
The arrest of the villain by Jamal is done poorly, despite Jamal's being a trained police officer in a specialist unit.