Characters are shown smoking filter cigarettes during the WW2 period. Although these were invented in the 1920s they were not generally available in the UK until the 1950s.
Filter-tip cigarettes were not introduced until the 1950s, yet Dorothy is shown smoking one at 24:10.
Mike says he's read all his father's books - but doesn't apparently realise that some (most?) of them were published after 1942 when Dorothy told Mike his father had died.