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?
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.