During the part of "Funniest Joke in the World" sketch that takes place in WWII, a news reporter holds a handheld microphone which is too modern for WWII, and a Bedford RL truck and Ferret armoured appear in some stock footage, both were introduced after WWII.
During the "Funniest Joke in the World" sketch, the narrator says that in autumn 1944 the Germans worked on creating their own lethal joke and by December it was ready and Hitler gave the order for the joke to be broadcast in English. The next scene, showing two English civilians listening to the joke over the radio, features the subtitle "1942... Somewhere in London"
In the "Funniest Joke in the World" sketch, the crack Inspector from Scotland Yard wears only one pip on his epaulets. Police Inspectors wear two pips on their shoulder, no British police rank insignia contains only one pip. Also the badge on his cap is not the Brunswick star used by the Metropolitan Police (which he would be a member of if he was from Scotland Yard).
During the Modern Artists' bicycle race, the artists are cycling towards John Cleese and therefore the artist's canvases will be facing away from John which means he could not see the paintings and unable to describe the paintings.