When we first see Andrew Foyle and Rex Talbot they are flying Spitfire Mk. IX's, but when they land at their home base they are flying Spitfire Mk. I's, which is the correct version for the Battle of Britain period.
In this episode, set in 1940, Foyle's son is flying a Spitfire that has markings of the 317 Polish Squadron "City of Wilno". The squadron was not formed until February 1941 and was not flying Spitfires until October 1941.
The clock used to set off the bomb in the suitcase has a large second hand which moves in 1-second jumps, indicating a quartz movement. Quartz clocks weren't available commercially until about 30 years later.
The Spitfire Andrew Foyle is shown flying bears the insignia of No. 317 Polish Fighter Squadron. However, this episode is set in September 1940, but 317 Squadron wasn't formed until February 1941.
During the investigation Foyle interviews witnesses involved with the crime, one of which was his son Andrew. This poses a clear conflict of interest. Whilst making for an interesting plot extension to family tension, would not have happened and Foyle would have to declare the relationship.