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 Germans - S1-E6
Deliberate mistake: When Basil asks Manuel to pull the hose on the fire extinguisher, the top of the hose falls off easily, resulting Basil to be squirted in the face. The bit where the hose is attached to squirts water out diagonally, but this would cause water not to go down the hose. This fire extinguisher was especially constructed to make sure the water was directed at Basil's face.
Answer: It's "Leisure Complex" by Dave Gold and Gordon Rees. Can be found on YouTube. The relevant clip is around 25 seconds in.