Plot hole: The fact that David becomes conscious after being hit and left back is dramatically fine but there is no aftermath - he misses to finish dealing with Ali and friends at that point.
Continuity mistake: The remote control of the hi-fi teleports between shots when Kate visits Ali at home. Ali leaves it next to the wall (along with the other remote), but it's not there anymore when Kate gets the remote of the telly some shots later.
Factual error: When Ali goes to see the Queen for the first time the voice over says "Her Majesty the Queen," while showing the outside of Buckingham Palace which implies that the next shot is of them inside. There is one problem here, the Queen's Royal Standard is not on the top of the Palace which it should be if she is there.David Mercier
Continuity mistake: When the fit refugees are shown to be examined upon their arrival at Dover, the officer in the background is seen to be turning towards the entry door twice during the subsequent shots.
Continuity mistake: In the scene where Ali walks to the floor of the House of Commons, he walks past Charles Dance and Michael Gambon and they say something like "What is he doing..." Look at the guy next to Charles Dance, he has his right hand on his face but immediately in the next shot he is gesturing with it and waving papers with the other hand.David Mercier
Continuity mistake: When the PM shows Ali the red button, the alignment of the newspapers on his desk changes between shots.
Continuity mistake: In the scene where Ali is at the center with the kids, he gives some yellow stickers to one of them and the kid sticks them to his arm. But in the next few shots the stickers keep changing their position on the kid's arm.
Factual error: The first newscast about the African incident displays Burkina Faso as "Burkina" on the map. This shortened name is not used for this country (AFAIK).