Bananas were freely available for Sam and Adam, but they were rationed and almost unobtainable until the early 1950s.
As Sam and Adam are walking to dinner, they walk through a very tidy demolition site with of bombing debris. The loose single bricks show no mortar, and the workmen have decided the best way to put the rubbish in the truck bed is to throw two bricks at a time to one another.
There are some left hand salutes from police officers about 15 minutes in.
In the chase at the beginning of the episode, the escaped prisoner is cornered on a disused railway viaduct. These would have been pretty much unknown at the time - before the Beeching cuts of the 1960s.
In the same scene, the camera cuts to a shot of a Red Kite circling overhead. Again, these were unknown in England then, although common now. They were reintroduced in the early 1990s.
Although it is 1945, a 1948 Rover P3 75 Sports Saloon can be spotted in one of the scenes.
Sam places a number of large drawings into a portfolio by holding them with one hand instead of two and putting a huge semi-circular crease in all of them by mishandling them in this way. If she had been working for the artist for more than a day or two she would know better than to handle things that way.