The tax disk in the windscreen of Foyle's car is shown in close-up a couple of times and is seen to be essentially blank, rather than being printed with an orange diagonal band which would have been correct for 1940.
The uniformed Superintendent is seen wearing the ribbon of the Police Exemplary Service Medal. This medal was not instituted until 14 June 1951, eleven years after the events portrayed.
The photo portrait of King George VI, taken by the renowned photographer Yousuf Karsh, is seen hanging on the wall of Foyle's office in May 1940. This picture wasn't actually taken by Karsh until September 1943. (The same photo is also seen hanging in Foyle's office in many episodes.)
The grounds of the White Feather Hotel has daffodils in flower in what is supposed to be late May 1940 (the Dunkirk evacuation period). On the south coast of England they would have all flowered and died by this time of year.
Foyle reads a letter from his son, in which Andrew writes "... I'll get a bit of leave before my wings exam." The photograph of Andrew, next to Foyle's chair, shows him wearing wings already.
One of the members of the Friday Club at the hotel is introduced as "the Right Honourable John Mowbray, son of Lord Mowbray". As the son of a Lord he is Honourable, but only Lords themselves, members of the Privy Council and a few others are Right Honourable.