Goodbye Mrs. Slocombe - S10-E1
Revealing mistake: At the end during the credits, Mr. Humphries and the Lady he played are onscreen at the same time and you can see the splice made to allow that to happen.
The Hold Up - S10-E3
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.
The Hold Up - S10-E3
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).
Revealing mistake: At the very beginning while the opening jingle is still going on, the camera cuts to Mr. Spooner standing behind the counter; he remains motionless, coat in hand, for a second or two before getting his cue to walk across the floor and begin the show.
Revealing mistake: When Mr. Humphries is talking to the canteen manageress about her lines as the hat check girl, in the shots of the former one can see Mr. Harman standing about in the background, waiting and watching for his cue to come on.
Character mistake: When Mrs. Slocombe volunteers to sing while Captain Peacock plays piano, Mr. Humphries responds that he didn't know she could sing, even though the department staff has been involved in many musical numbers over the series.
Friends and Neighbours - S10-E6
Revealing mistake: When Mrs. Slocombe's cat is supposed to be under the hat and "eats" the clockwork mouse, it is clear that it's a machine. This is most obvious when the hat spits out the mouse and slightly rises up in the front, which shows the wheels.
Answer: That wasn't possible in 1972. Until recently squatting was a civil offence in the UK, not a criminal one, and removing squatters was a complex and time consuming business.