When Andrew Foyle is in Wing Commander Turner's office there is a model Spitfire on Turner's desk in front of him. From the reverse angle shot it is replaced with a model of an airman.
Andrew Foyle's age was established as 22 in 1940, meaning he was born in 1918.
The birth date on his mother Rosalind Foyle's grave is given as June 1902. This would make her 15-16 years old when he was born, and would certainly have been only 15 when he was conceived. The age of consent in the UK has been 16 since 1885.
When Andrew and Sam are in the pub, Andrew's hair is messy and fluffy that completely covers his forehead as he leaves and Sam kisses him. Andrew arrives at home still with Sam's lipstick on his cheek but his hair is flattened and neatly combed with just a bit of hair on his forehead.
Wing Commander Turner selects airman Greville Woods to fly a night reconnaissance mission using a new camera that can photograph heat but as his Spitfire is out of action he is given Andrew Foyle's instead and flies off that evening. However both men are fighter pilots. A standard Spitfire fighter would be useless for reconnaissance and it would takes several days at least to refit it to take any type of camera. For reconnaissance missions, specially fitted out planes were used that had cameras in the belly and wings instead of armaments. These were flown by dedicated reconnaissance pilots who were trained on how to take photographs from the air.
Foyle is shown fly-fishing a stream. A few minutes there is snow on the ground in a garden indicating winter. The fly-fishing season is in summer months, traditionally April to September.
Andrew is told that he is being transferred to 605 Squadron to teach and subsequently flies off to join them at Debden, Essex. However 605 was a combat squadron at the time, not a training unit, from February 1941 they were stations at RAF Martlesham Heath, Suffolk, and they were frying Hawker Hurricane Mk.IIa at the time so would have had little use for Andrew's Spitfire.
An enormous ornamental stone lion falls 50 feet from the roof of a building onto the bonnet of a car and bounces off, leaving not so much as a scratch or a dent on the car.
Two characters are identified as Aircraftsmen in the credits. They are in fact Aircraftmen (men of aircraft, not craftsmen of the air). (Even RAF personnel sometimes make this error - but error it is!)
When fixing the fuse in Dr Wrenn's house, Gordon Drake refers to it as a ring main fuse. Ring mains did not start to be introduced in the UK until after World War II. In February 1941 (when this episode is set) it was at least a year before the ring main concept was even being discussed in the government's Electrical Installations Committee, which was convened in 1942 and reported in 1944. But as it was a lighting fuse, a ring main would not be used even now. Also, a 3 amp fuse was very unlikely for a lighting circuit - the common fuse for a radial lighting circuit would have been 5 amps.
Andrew Foyle's Spitfire has the City of Wilno emblem on the side of the cockpit, indicating that it is part of Polish Air Force 317 Squadron - a unit that did not have Spitfire's until the end of 1941. (The same Spitfire has been used in previous episodes.)