The Dead Parrot Sketch was based on an experience Graham Chapman had with a used car salesman who categorically refused to acknowledge that there was anything wrong with the car, even when Chapman showed him that there was. Chapman and John Cleese wrote this experience as a sketch for an earlier television show, but always felt that there was a way to make it funnier. They eventually decided on substituting a deceased pet for a broken car, and thus the Pythons' most famous sketch was born.
The "Dead Parrot Sketch" was based, in part, on a drama school exercise/game in which two actors improvised dialogue, the object of which was for one participant to try to get the other to repeat a line without himself repeating. The first person to repeat is the "loser" of the game. Tom Stoppard, in his Rosencrantz & Guildenstern Are Dead (1990) featured a more elaborate version of this exercise which is cited in the quotes section for that movie.
Several sketches from this episode were reshot for the feature film Monty Python's and Now for Something Completely Different (1971) including The Parrot Sketch and Hell's Grannies. In addition, the basic framework of the Colonel (Graham Chapman) interrupting the show when it got "too silly" was used in the film.
While writing the Parrot Sketch, Graham Chapman suggested that "Norwegian blue" would be a humorous name for a species of parrot, given that they are normally found in warmer climates. Surprisingly, however, recent scientific discoveries indicate that there was a species of blue parrot native to Scandinavia, though it would have lived fifty five million years ago.
The pet shop set was used again in a later episode for another sketch featuring Cleese and Palin.