Deliberate mistake: In nearly all the episodes that the front door of the hotel is open we see a painted board that is meant to be bushes or something outside. Yet whenever we see scenes from the outside of the hotel there is no sign of any trees or bushes.
Revealing mistake: Whenever somebody closes a door, leans against a wall, or goes up/down the stairs and brushes against the wall, it wobbles, revealing that the walls are lightweight stand-up props.
Visible crew/equipment: Near the start of the episode, after the guest has told Basil that he will only be staying until Sunday, Basil walks from the dining room to the office, and the shadow of the camera following Basil can be seen in the reflection of the studio lights in the picture above the Drawing Room door. (00:04:45)
Revealing mistake: When Manuel throws the grapefruit at the other guests, you can see the woman closest to the camera react before Manuel throws it. (00:11:00)
Revealing mistake: When Basil sends the grapefruit flying, we see Polly go through the doors to the kitchen. However, if you look closely at the doors as she goes through you will see just a plain wall. Not the kitchen as is seen in other episodes. (00:11:00)
Continuity mistake: When Basil brings in Lord Melbury's cases, they swap hands between the exterior and interior shots. (00:14:20)
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)
Visible crew/equipment: When the bald hotel guest asks Basil for his drinks and slams his hand on the table, in the next shot a boom mic can be seen briefly as it is pulled away. (00:24:05)
Visible crew/equipment: At the end of the episode where everyone is cleaning up, there is a shadow of the boom mic on the wall. (00:29:05)
Audio problem: Throughout the episode the picture Basil is distracted from putting up has no glass covering on it. However, when he smashes it at the end you can hear the distinct sound of glass breaking. (00:29:35)
The Builders - S1-E2
Deliberate mistake: When Basil is arguing with Polly and eventually decides to call O'Reilly, he trips over the gnome. However when we see Basil come out from behind the desk, he takes the gnome out of a side gap in the desk, perfectly out of reach of Basil tripping over it. (00:14:30)
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)
The Builders - S1-E2
Revealing mistake: When Basil smashes Manuel against the wall where the dining room is meant to be, we can see it is made out of cardboard. Notice how it begins to fall off, even though it is meant to be sealed and covered in wallpaper. (00:16:05)
Suggested correction: Perhaps this was due to O'Reilly's shoddy workmanship?
You could say that but Fawlty towers had wobbly sets all the time. I would say this would be covered under "mistakes".
Where is the 'codswallop' as you so euphemistically put it? To me it looks like O'Reilly cut corners by shoddily placing a sheet of plasterboard in the doorway without attaching it well then shoddily wallpapering over it. Hence the reason for it falling out.
The Builders - S1-E2
Revealing mistake: Look at the skirting board of the section of wall Basil hits Manuel against. There are black shoe marks on the paint from previous takes where Manuel kicks the board. (00:16:15)
The Builders - S1-E2
Revealing mistake: The umbrella Sybil uses to hit O'Reilly and Basil with is padded to protect the actors. (00:23:30)
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)
The Builders - S1-E2
Visible crew/equipment: When the Major says "He lost it you know" to Polly before entering the dining room, the silhouette of a boom mic can be seen on the top right hand of shot. (00:25:20)
The Builders - S1-E2
Visible crew/equipment: When Stubbs says to keep the door closed, a boom shadow is seen on the wall by the door. (00:27:20)
The Builders - S1-E2
Continuity mistake: When Sybil catches Basil with the closed-off dining room and they start an argument, the door to the rooms upstairs is closed, two shots later it is open, but nobody came or went that way during their conversation.
The Builders - S1-E2
Revealing mistake: In the scene where Polly brings Mr O'Reilly a cup of tea, it is obvious on several occasions that there is nothing at all in the cup. Not only does he hold it in such a way that you can see inside, but when Basil snatches it away nothing spills out.
Suggested correction: The sound isn't glass as you can see just as he goes to smash the picture there is no glass on the picture.