When Richard Hunter is in the pub reading the newspaper article about Howard Paige, another front page article describes the death on stage of an actress appearing in the Portsmouth Hippodrome. This incident actually occurred although it happened in 1936, not in 1940 as the newspaper indicates.
The comedy radio show that the desk sergeant listens to is It's That Man Again (known as ITMA) starring Tommy Handley. This was a staple radio show throughout the 1940s.
The wallpaper in the bedroom of Sam (played by Honeysuckle Weeks) is the pattern 'Honeysuckle' by William Morris.
The final outcome of the suspect in this case is revealed at the start of series 7 The Eternity Ring (2013).
At the end, Paige leaves in a RAF transport plane. The plane is the C 47 Skytrain, known to the RAF as the Dakota. This is the most famous military transport plane of WWII. There were versions for paratroopers, infantry, cargo, and fancied up VIP carriers. However, the first of the 2000 Dakotas delivered to the RAF arrived in 1942. The program hinges on the commitment of fifty US ships while it shows the RAF using the US McDonnell Douglas aircraft.