Visible crew/equipment: After Mr. Johnson refers to the Torquay guide as the 'world's shortest book' and leaves the hotel, you see a boom mic coming in at the top of the screen for about 3 seconds.
Visible crew/equipment: When Basil asks the family sitting by the window to move, a boom mic can be seen in the top right hand corner. (00:16:05)
The Builders - S1-E2
Continuity mistake: After hitting O'Reilly, Sybil goes to the desk and grabs the phone. In the first shot, Sybil grabs the phone with her right hand, she puts it next to her ear and then put her left hand on the microphone. She turns her back to Basil and O'Reilly. In the next shot, the phone has not been put next to the ear yet, while Sybil's left hand is not on the microphone but on the cable. (00:23:40)
Basil the Rat (a.k.a. Rats) - S2-E6
Revealing mistake: When Polly and Manuel are walking down Fawlty Towers drive with Basil the Rat in the box, there is an arch over the front entrance with Wooburn Grange Country Club written on it. This is the name off the building used as the location for the exterior scenes of Fawlty Towers; this is most visible on the DVD.
Basil the Rat (a.k.a. Rats) - S2-E6
Continuity mistake: When Basil and Sybil are talking to the public health inspector in the kitchen (on his second visit), Basil breaks two bottles of wine. When he removes the second bottle, there are two bottles remaining on the rack, but when the camera cuts away and then back when he breaks it, there is only one bottle left on the rack.
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.
The Builders - S1-E2
Revealing mistake: In the part where John Cleese is smacking Manuel's head against the place where the dining room doors are supposed to be, you can see very that Manuel is kicking the wall right when his head is supposed to hit it, creating the sound of his head hitting the wall. Check it out because it's very obvious and hard to miss. (00:16:05)
Visible crew/equipment: When they are in to see Sybil, as they switch on the light, the boom mike is visible on top of the screen.
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.
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Continuity mistake: When Manuel fetches Basil from outside, Basil enters the building first in the exterior shots, but Manuel gets to reception first in the interior ones. (00:01:30)
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Continuity mistake: When the guest from number 8 is going up, in one shot Basil is looking on his watch when you see him from behind but not from the front a split second later.
Continuity mistake: Near the beginning, when Sybil goes into the office after speaking to Basil about the date, the lights are obviously on in the office, but when she walks out, it can just be seen on the right that the office is in complete darkness, and then when the shot changes back to the regular one in the lobby, the office is lit up again, without anyone going in there in the meantime.
Visible crew/equipment: When the Hamilton's are talking to Sybil, Basil enters and Mrs Hamilton says 'Harry finds it too gloomy'. At the top of the screen the boom mic is visible.
The Germans - S1-E6
Other mistake: When Basil shuts Manuel in the burning kitchen and slams the door, the walls shake.
The Wedding Party (a.k.a. Sex) - S1-E3
Visible crew/equipment: Just after Basil and an old woman leave the kitchen, the scene cuts to the interior of Mr. Lloyd's room. As soon as the first shot of the interior begins, a boom mic is visible for a split second at the bottom of shot. (00:20:40)
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Visible crew/equipment: When they discover that Ms. Tibbs has fainted in the office the boom mike shadow is visible on the wall to the right.
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.
Visible crew/equipment: When Basil says to Mr. Hamilton "I'm sorry if it wasn't wide enough for you, a lot of the English cars have steering wheels" the boom mic can be seen in the top left corner.
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Visible crew/equipment: At the start of the episode, when Basil follows Manuel into the hotel, the shadow of a crew member holding a boom mic can be seen bottom right as the camera follows them across the terrain. (00:01:30)
Communication Problems (a.k.a. Theft) - S2-E1
Continuity mistake: During the opening scene where Polly is arguing with Mrs Richards over "giving change", the loose papers on the reception counter keep disappearing and re-appearing between shots.
Answer: It's "Leisure Complex" by Dave Gold and Gordon Rees. Can be found on YouTube. The relevant clip is around 25 seconds in.