Question: Why does Foyle wear an overcoat at all times of the year? I know that the English summer is temperate, but always a long, floppy overcoat?
Answer: An early photograph of Andrew Foyle shows him wearing his 'wings' before qualifying. R D F was referred to as Radar, but the term Radar was not used until 2 years later.
Question: Why do a lot of police officers and army personnel have holes where certain badges should be on their shoulder straps on the uniforms?
Answer: The in-story answer is that these people have been promoted from lower ranks with more badges to higher ranks with fewer, e.g., Captain (three stars) to Major (one crown) or Chief Inspector to Superintendent. The show-making answer is that the costumes are genuine but used to have different ranks to the ones worn by the characters.
Answer: He doesn't actually wear it all the time even in summer. In some episodes in the summer he simply wears his suit with jacket.