Revealing mistake: When Basil is climbing up the ladder to view the inside of Mr Johnson's room, he accidently peers inside Dr Abbott's room. When he starts doing his "checking" routine on the window before he falls backwards, the pane flexes, indicating that it's made of clear perspex.
Revealing mistake: There are noticable disparaties between the locations of rooms and the windows on the outside of the building. This is particularly noticable in this episode when Basil climbs a ladder to look through the window.
Revealing mistake: When Basil sneaks into Raylene's room to listen for the "extra guest" in Johnson's room, Raylene wakes up screaming. When Sybil comes in, turns the light on and Basil says "I didn't know she was there, I just came in to check the walls", look at the extreme right of the screen. You can see the shadow of a boom light on the wall.
Answer: It's "Leisure Complex" by Dave Gold and Gordon Rees. Can be found on YouTube. The relevant clip is around 25 seconds in.