Enforced Method Acting: The infamous Mr. Creosote scene was filmed in a warehouse with no air conditioning and a dairy-based prop vomit that went bad after several days of shooting. This, combined with the content of the sketch itself, made the extras very nauseous and several of them (including one in the bottom right-hand corner) can be seen actually vomiting as they exit the restaurant covered in Creosote's remains.
Hollywood Accounting: Eric Idle, on his Exploits Monty Python concert tour at the Turn of the Millennium, noted that this movie was the only Python film made with major studio backing (Universal Pictures)...and thus the only one that apparently didn't turn a profit. So in this tour's version of "The Crimson Permanent Assurance", there's an additional verse about studio accountants.
Technology Marches On: The "Birth]]" sketch was, at the time, a cutting satire on what was seen as unnecessary spending on medical equipment. Nowadays, anyone who's seen a modern medical drama, with the surgeons surrounded by massive banks of electronic equipment, may wonder what all the fuss is about — to the point that operating without such equipment nowadays would be seen as unusual and dangerous. Other parts of the sketch though remain relevant.
Also, Cleese and Chapman tell the woman after the birth that she can get a video of the birth of her child on VHS and Betamax!
... and Super 8mm film!
Throw It In: The line, "Hey, I didn't eat the mousse!" was an ad lib.
The second verse of "The Galaxy Song" was meant to be an animated sequence along with the instrumental part, but Terry Gilliam opted out of animating it in favor of shooting more of "The Crimson Permanent Assurance".
According to the DVD audio commentary, the Arthur Jarrett segment was a remnant of a previous draft of the film, where all of Monty Python were going to be convicted at the beginning of the film for trying to use it as a tax dodge, and each be sentenced to death in a manner of their choosing.
Two involving Mr. Creosote.
The sketch almost didn't make it into the film. Terry Jones' first write-up of the sketch with Michael Palin fell flat and had to be re-written by Graham Chapman and John Cleese (who saved the sketch from being binned because he wanted to play the head waiter, whom he thought had the funniest part).
Jones initially wanted Gilliam to play Mr. Creosote. Gilliam persuaded Jones to play the character instead.