Plot hole: When the robbers come onto the floor and go into Mr. Rumbold's office, the staff suggests calling the police, only to be told by Mr. Harman that the only outside line is in Rumbold's office. This, despite the fact that there have been numerous occasions throughout the series where characters made and received personal calls on the department phones (Mrs. Slocombe calling her cat, Mr. Humphries calling his mother, etc).
Other mistake: There is another counter on the floor, to the right of the stairs, that is usually staffed by two women besides Ms. Brahms and Mrs. Slocombe. But throughout the show when there is a on-floor meeting for the entire floor staff, these two are never included in the discussions.
Continuity mistake: When the robbers have nodded off and Mr. Spooner and Cpt. Peacock cut themselves out of the rope tying them to the cabinet, a clock outside is sounding the hour; if one listens it chimes nine times. But minutes later, after the rest of the group have come in and they make the call to Mr. Rumbold, the latter exclaims "It's after midnight." upon answering the phone even though less than ten minutes have passed.
Continuity mistake: Mr. Lucas says the figures for the previous Monday were 325 pounds, and at that point in the day the departments combined (170 and 150) were up to 320, five pounds short. However, later when Mr. Rumbold is talking to Mr. Grace about the sudden drop in sales, he says they are "still 20 pounds short" of the previous Monday.
Other mistake: The gender of Mrs Slocombe's cat is always different in each episode. Sometimes her cat is a female and other times it is a male. (eg. In 'Mrs Slocombe Expects', her cat is female. In 'No Sale', when Mrs. Slocombe complains about her having to get up to have a bath at 6:00 in the morning, she says, "The gurgling of the tank woke him up.").
Revealing mistake: When Mr. Lucas gives Mrs. Slocombe the radio mike, it slips down her dress out of reach; Mr. Harman says "It can't have gone down all that far," and he's right: The short cord of the mike is visible sticking out of the dress for quite some time until Mrs. Slocombe herself pushes the mike down (in the appearance of trying to fish it out).
Audio problem: At the end when Capt. Peacock comes onto the floor in his maintenance garb, Mr. Harman points him to a spot on the floor and tells him to mop it up. In the initial shot Harman is indeed telling him, but when the camera cuts to another angle Harman is visible and still talking but his lips aren't moving.