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.
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 Kipper and the Corpse (a.k.a. Death) - S2-E4
Revealing mistake: The dog's mouth is nowhere near Manuel when he is "bit".
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Visible crew/equipment: When Polly is on the phone with the undertaker and she says "I'm afraid somebody's died tonight", the boom mike is visible to the right of the screen.
Continuity mistake: In this episode, Basil hides in a closet to try and trap a girl staying the night in a guest's room. However, in other episodes ("Wedding Guests," "Communication Problems," and "The Kipper and the Corpse"), there is a room in the same spot the closet is in this episode.
Continuity mistake: After the woman screams, Sybil knocks the wall and you can see it move.
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)
Visible crew/equipment: When Virginia shows the cakes she's brought with her the boom mike is visible above them.
Continuity mistake: When Basil brings the Hamilton's their bottle of wine, he fills up Mr Hamilton's glass but not Mrs Hamilton's. However, a couple of shots later, we see both Mr and Mrs Hamilton drinking wine from their glasses despite nobody pouring any wine into Mrs Hamilton's glass.
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Revealing mistake: When the characters are in Mr Lehman's room discussing his death, the backdrop outside the window has clear wrinkles and fold marks in it even though it's supposed to look like the outside.
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)
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)
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)
The Builders - S1-E2
Other mistake: In the end credits, Major Gowen's surname is incorrectly spelled "Gowan."
Continuity mistake: In the episode "The Wedding Party", the first two rooms on the second floor right of the stairs were 11 and 12. Yet in this episode, those two exact same rooms are now 5 and 6. (00:19:20)