In the department store where Alastair Sim goes to shoplift, there is a large sign over the entrance doors reading Swan & Edgar. A blatant example of advertising, as of course stores have their names on the outside, not the inside.
When the newspaper headline shows Herbert Russell foiling the bank robbery, there are two headlines of other articles on the newspaper page from when Herbert was in a train earlier and saw the headline of a bank robber being sent to jail.
When Deniston Russell comes up before Sir Charles Robson, Sir Charles should recuse himself from the case since he knows the defendant: Russell is engaged to be married to his daughter.
When Deniston Russell visits the police station for the second time, he addresses the officer on duty as Inspector. However, the man has three arrow-shaped stripes on his shoulder, which clearly marks him as a Sergeant. Even if he didn't know the difference, one would expect the police officer to correct him.