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)
Visible crew/equipment: When the Hamiltons arrive, Mrs Hamilton says 'May I introduce my husband.' The boom mic is seen at the top of the screen.
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.
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.
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: In the scene where Basil and Manuel have put the corpse in the room behind the reception, and the Major comes over and speaks to Basil, the actor playing the corpse blinks.
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Character mistake: When Sybil is telling Basil that the two men and the woman are coming to collect Mr Leeman but he's already pronounced dead, she tells her husband that they are coming to collect him "at lunchtime". However, his colleagues told Mr Leeman they'd collect him at 9:30 and not lunchtime.
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Revealing mistake: Just after Polly comes down to to the kitchen to tell Sybil that Mr Leeman's dead and they leave, Basil wanders back in, to learn the news. Watch the wall on the right on the staircase when Basil shoves past Sybil on the stairs. The wall shakes so much at that point it's virtually impossible to miss.
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Visible crew/equipment: In the kitchen scene with Basil, Sybil and chef, Basil says, "Would you believe it, I give him his breakfast, I take it all the way upstairs." At this point, the shadow of a boom microphone on the wall to the right is visible.
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Revealing mistake: When Basil, Manuel and Polly are trying to hide Mr. Leeman from the other guests, they put him in a cupboard. While they are talking to the people staying in the room, Mr. Leeman's hand comes out of the cupboard. Watch carefully, and you can see the actor opening the door from the inside, and then putting his arm down, making him look like the corpse.
The Kipper and the Corpse (a.k.a. Death) - S2-E4
Visible crew/equipment: When Mr. White asks if Basil can clean their room later the boom mike shadow is visible on the door behind Mr. White.
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.
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.
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.
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 Kipper and the Corpse (a.k.a. Death) - S2-E4
Visible crew/equipment: When Basil, Manuel and Sybil enter the office and find Miss Tibbs fainted next to the corpse, the boom mic appears on the righthand side of the screen next to the fan on the wall. And when the camera switches back to the full shot of all the characters, the boom mic appears again.
Answer: It's "Leisure Complex" by Dave Gold and Gordon Rees. Can be found on YouTube. The relevant clip is around 25 seconds in.