Plot hole: In the Upper Class Twit of the Year Show, there are five contestants. However, after Oliver runs himself over, in the events that follow there are only four props for the remaining twits (four mannequins, rabbits, and guns); since Oliver's death was unforeseen, shouldn't there be five of each? (This mistake, by the way, is rectified in the film version of this sketch).
Factual error: When the allies are testing their joke on the private in the field, just before he starts laughing at it, a bright red car drives past behind him. You can see it in a break in the trees. This sketch is set in WW2, and the car is obviously not from that era.
Continuity mistake: At the start of the interview sketch, and at several times throughout, Cleese says he's interviewing people for a management training course. At the end, however, he suddenly claims it was a job interview.
Other mistake: William Knickers' letter, complaining about the sketches, starts "I strongly object ..." but the voiceover says "I object strongly ..."
Continuity mistake: At the beginning of the vegetarian restaurant sketch, Eric Idle stands right behind the pointy sculpture. It is quite short and in some shots the points of it are visible right at the bottom of the screen, but in other shots people stand and walk through right where it is meant to be. And in the final shot, when Eric is complaining about the punchline, it is definitely gone.