Continuity mistake: When Basil brings in Lord Melbury's cases, they swap hands between the exterior and interior shots. (00:14:20)
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
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
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.
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.
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)
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Continuity mistake: There appears to be a very obvious splice edit in this episode. When Basil manages to get Kurt off him after being pinned to the kitchen table, he pushes Kurt against the wall knocking him out. Before this Basil is lying flat on the table and we never see him get up to a standing position beforehand.
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Continuity mistake: When Basil goes to fetch the branch to give the car a thrashing after it breaks down, the car manages to move onto the pavement all by itself.
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Continuity mistake: When Basil is driving home the second time, he is turning into a street where a van is parked. When he turns the street is dry. In the next scene where he is backing away from the van, the street is all wet.
Gourmet Night (a.k.a. Gourmet's Paradise) - S1-E5
Continuity mistake: When Basil's car breaks down for the final time after reversing away from the van, watch closely on the garden path of the house right next to the car. The garden gate is open, and you can see it swing shut (look at the black shape just above the hedge) just as Basil says "One, two three." The gate was shut when he first reversed around the corner, but was open again after the shot cuts back to the car (after it's moved to the right along the pavement).
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.
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.
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)
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.
Continuity mistake: When Basil is talking to Mr. Hamilton in the dining room there is smoke coming from the kitchen. The next moment he goes into the kitchen and all the smoke is gone. (00:24:00 - 00:25:00)
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
Continuity mistake: When Basil, Polly and Manuel are trying to hide the body in the cupboard in the guests' bedroom, the door behind them leading to the bathroom mysteriously opens and closes between shots throughout the scene.
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.
Answer: It's "Leisure Complex" by Dave Gold and Gordon Rees. Can be found on YouTube. The relevant clip is around 25 seconds in.