The code name for the British Intelligence secret service was "The Circus". John le Carré told the producer that the BBC offices matched his image of the Circus, and so parts of the Circus office interiors were filmed in the offices of the BBC.
John le Carré has admitted that the vocabulary used in the novels/series (babysitters, lamplighters, the Circus, the nursery, moles) was made up. He was later amused to discover that real agents had begun to appropriate some of his vocabulary once his espionage stories were published.
John le Carré's 'Tinker, Tailor, Soldier, Spy' novel, was based on the uncovering, during the 1950s and 60s, of the Cambridge Five traitors who were KGB moles working within the SIS.
In episode 5, Fawn's hair is shaggy and hangs over his ears. A day later (in episode 6) it is short and trim. He's been guarding the kidnapped Toby Esterhase for the intervening period, so he could hardly have run out and got it cut.
During the outdoor daytime scene where Smiley converses with Prideaux, they are tracked by the camera as they walk across a field. At one point, when they are nearest the camera, the shadows of some crew members are just about visible on Prideaux's coat.
Jim Prideaux goes off on his abortive mission to Czechoslovakia at the end of March. Following this scene is a strap-line that says "six months later". That should put the continuing action at the end of September. However we see snow on the roads, and Roddy Martindale saying to George Smiley in the restaurant "... I do hope you're not going to tip him. It's a guinea at Christmas".