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
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.
The Builders - S1-E2
Continuity mistake: Towards the end of the episode, a couple of scenes before Mr Stubbs arrives, we see Basil start up the tape player prior to hiding in the kitchen. The garden gnome on the desk is right next to the tape player at this point. When Sybil turns the tape off the player has rotated 45 degrees or so (despite nobody else having come into reception in the intervening time) and the gnome is now further along the desk towards the camera as we look on the wide shot. The gnome in the next shot is seen beside the checking-in book when Basil wanders out of and back into the office a couple of scenes later, yet when Mr Stubbs is asking about the lintel for the new door shortly after that and we see Sybil writing in the book, the gnome has moved out of shot altogether.
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: 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)
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Audio problem: When Basil impersonates the duck, the sound effect used continues when his mouth is closed.
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)
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)
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 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)
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)
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.
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Visible crew/equipment: At the end, the stage lights can be seen in the silver lid. (00:29:00)
The Germans - S1-E6
Continuity mistake: When Basil is being pursued by the doctor, the left antler on the moose's head on the wall is broken. When the head lands on Manuel, the antler is not broken or limp any longer, and when the Major wraps the head on the snout, the antler breaks and goes limp again.
The Builders - S1-E2
Continuity mistake: When Basil rushes out of the hotel to see Sybil, his shirt is fully buttoned, but when Basil is seen running down the steps, he has one more shirt button undone than when he was inside.
The Builders - S1-E2
Visible crew/equipment: When Polly passes Basil the stapler, a boom mic can be seen lifting up out of shot in the top left corner of the screen.
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
Revealing mistake: The umbrella Sybil uses to hit O'Reilly and Basil with is padded to protect the actors. (00:23:30)
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.