During the waiter's strike it appears to be daytime inside the great hall and night time outside.
Anthony Blunt is referred to as a relative by the Prince of Wales (Edward VIII). Blunt was actually a second cousin of Elizabeth wife of George VI (later the Queen Mother) and not related to the Windsors at all.
Spanish Civil War began in 1936. Prince of Wales became Edward VIII in January of that year. The prince could not have been at aristocrat's house after the war had begun.
Anthony Blunt is given a sporran by "Queen Mary". The Queen he is seen conferring with several times is Queen Elizabeth, later the Queen Mother.
There is a scene with a steam train leaving a station during World War 2 with the blue double-oval "First" sign (for First Class) on the window and the red triangle "No Smoking" sign also on a window. Both these signs were not introduced until the railways were nationalized in 1948 and became British Railways.
An exterior shot in Cambridge prominently features black-and-gold pedestrian signposts that did not appear in English cities until several decades later.
In the very first scene, in the chapel, the choirs lips do not match what they are singing.
Guy Burgess is in a London flat eating Van Camps baked beans from a can. This brand is not available in England.