Although the siege lasts for only a few hours in the movie, Stubbs' (Sean Pertwee) hair is noticeably longer after the first scene he appears in.
When Alan is shot and dribbling down his face, the spit disappears after a quick cut away from him.
When Alan first goes into the room with the hostages Jason Tresswell get up and speaks twice - once in the background and then again in a closeup scene.
Alan's JUST SACK PAT page that he writes at the meeting changes after he drops his gloves. It is noticeable on the S and the P. The change is likely because the shape of Alan's P is a plot point later in the movie.
When Alan drops his driving gloves on the way out of the board meeting, the way they're arranged on the floor changes between shots.
Tasing someone causes all the muscles in their body to contract, therefore tasing someone with their finger on the trigger of a loaded weapon would cause them to involuntarily fire it.
The Chief Constable has a lot more medal ribbons on her uniform than is usual for British police officers. Although ones who are ex-military are entitled to wear medals earned during their previous service, the amount she has still isn't credible, especially for someone who looks so young.
Alan tells us the time is one minute to noon, however the clock reads 11 o'clock.