When Ray tells Bruce that he will apply for the Inspector position, Bruce burns a hole into the couch with his cigarette. In the next shot, the cigarette is completely lit, with a full amount of ashes at the top.
In the bedroom at Ocky's flat, Bruce lifts the inhaler and the dark blue cap is on, but he immediately snaps it up and takes a puff without removing the cap.
As Lennox prepares to tell Robertson that he's applying for the job of inspector ("I'm letting you know first"), James McAvoy's right hand changes position rapidly between shots.
While on holiday in Hamburg, Bladesey reads from his guidebook and tells Bruce that modern Germany has existed since 1865. German unification happened in 1871.
When Robertson writes homophobic graffiti about Inglis in the male toilets (and then blames someone else), Insp. Toal says that this is not discrimination if Inglis isn't actually gay. In fact, this would be "discrimination by perception".