Continuity mistake: During the Ministry of Silly Walks sketch, in the office, John Cleese pulls out a film-projector from his desk, and you can see the power cord plugged into the back of it. After the spoof black-and-white film footage showing the silly walks, John Cleese throws the projector away. The power cord, which was originally plugged in, has disappeared completely.
Other mistake: The final 'How to Recognise' announcement is originally written as "Number thirty. The End." When the show was broadcast, it was "Number thirty one. The End", yet all the other numbering tallies with the script. So either Cleese miscounted on the night of recording or they inserted another one which was later cut.