Londoners hurrying to an air raid shelter in 1940 pass a wall sign for the Royal Festival Hall, opened in 1951.
In the opening scene, the British are shown using a bazooka-like weapon to knock out the tank column. In 1940, there was no such thing as the weapon seen here.
When the conspirators are on the terrace of the pub, the Telecom Tower can clearly be seen in the distance to the left of Tower Bridge. Construction on the tower didn't begin until 1961.
A London bus wouldn't show LONDON on the roll sign for the route's endpoint, but rather a specific place within London.
In the Dunkirk scenes in the beginning of the film, most of the rifles carried by the British troops are not Lee Enfield 303's, judging by the sling fitting they might well be German rifles or possibly Italian ones.
Nobody, military or civilian, carries a gas mask.
Spitfires, models or replicas perhaps, appear in German markings.
In the early scenes of Dunkirk evacuation, a Union Jack is shown flying on a British ship. Ships of the Royal Navy flew the white ensign and merchant ships the red ensign.
The "Spitfires" in RAF roundels are actually Hispano Buchons, a Spanish-built derivative of the Messerschmitt 109, while the Messerschmitt 109s are portrayed by Spitfires (either real or models) painted in Luftwaffe colours.