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)
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.
Revealing mistake: When Basil is out of the car and shouting at it after its final breakdown, you can see a crew member reflected in the right hand side of the windscreen giving John Cleese cues. It's not Cleese himself, as the reflection remains after he runs out of shot to get the tree branch, and the reflection doesn't mimic every action performed on screen.
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).
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.
Visible crew/equipment: Just after Basil gets the duck from Andre, he tells Manuel to get the trolley. Basil then walks into the door, and the duck goes flying. You can briefly see the arm of the crewman holding the door closed. A few seconds later, Manuel comes through the door and stands on the duck. For about 5 seconds you can see the crewman's face.