After Mrs. Richards bumps her head in the hotel office, Basil picks up a bit of something from off the floor and asks, "Is this a piece of your brain?" John Cleese was going to cut this joke before the show aired, but Andrew Sachs convinced him to leave it in. (It gets one of the biggest laughs from the audience for this episode.)
John Cleese was very good friends with Joan Sanderson. He specifically wrote the role of Mrs. Richards for her. She was very reluctant to take the role as she is the polar opposite of the character and felt bad for being so miserable. This is the exact reason why Cleese wanted her to play the part. He convinced her to take the part. Cleese was delighted with her performance and stated this is his favorite episode of the series.
Series 2 aired roughly four years after Series 1 of the show, by which time John Cleese (Basil Fawlty) and Connie Booth (Polly) had recently divorced after ten years of marriage.
The cast features three of John Cleese's "wives". Connie Booth (Polly) was his wife in real life (though they divorced in 1978, roughly a year before this episode), Prunella Scales played his wife in this show, and Joan Sanderson (Mrs. Richards) played his wife in The Great Muppet Caper (1981).
When Sybil throws the cup of tea over her husband, she actually almost misses him entirely, but catches the Major who is standing behind Basil square in the face.