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.
In episode 6, when Peter Guillam is testing the taping system at the safe house, he says the recorder is voice-activated, but it doesn't stop turning on his first silent pause, which is much longer than his second and third pauses, when it stops instantly.
In episode 6, Bill Hayden writes a cheque for his girlfriend and tears it out of the cheque-book. He then writes her name and address on a slip of paper. In the next shot he is shown ripping a (blank) cheque from the cheque-book and handing it to Smiley along with the slip of paper.
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".
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.