Bad Export for You: Averted with the original episode package that aired on PBS in The '70s. The episodes were taken from the master tapes and not the BBC broadcast tapes, which meant that several of the cut scenes mentioned in the Executive Meddling entry below were untouched in the PBS version.
Defictionalization: Several things, but perhaps most prominently the "Silly Party" of the Election Night Sketch inspired the Real Life Monster Raving Loony Party. The Overly Long Name of a candidate was also borrowed by a real British election candidate.
In the "Mouse Problem" sketch from Episode 2, the address and phone number of an interview subject who has admitted to wanting to be a mouse are displayed and read out by John Cleese. In the original broadcast from 1969, the phone number was David Frost's home phone number, and after fielding a large number of prank calls, an annoyed Frost complained to the BBC, who edited the number out of the first re-runs in August 1970.
In the first run (1973), show no. 38 started with a Party Political Broadcast that was choreographed. Upon the syndication rights changing in 1983, the brainiacs at Time-Life (first syndicators) erased it. It was replaced with brief superimposed titles. The first DVD release of the Monty Python 16-Ton Megaset delivered an even worse blow: the previews of BBC comedies ("Dad's Pooves", "Up The Palace", etc.) at the end were left out.
Executive Meddling: The BBC frequently got cold feet over some of the Pythons' humour, resulting in often awkward acts of censorship.
If the episode with the Tudor porn shop seems disjointed, that's because it had to be edited rather severely before it was allowed to air.
The "Political Choreographers" sketch was edited out of one episode after its initial broadcast and apparently only survives in a low-quality off-air recording.
Additionally, most episodes of the two Python precursor series, Do Not Adjust Your Set and At Last The 1948 Show, have been wiped. This could have happened to Flying Circus itself were it not for the actions of Terry Gilliam, who bought the masters as soon as he could.
There is an animated section in between the "Crackpot Religions" sketch and "How Not to Be Seen" involving Jesus and the two thieves being crucified on telephone poles, while an Alter Kocker Satan (played by Idle) appears out of the ground. It was cut after its initial showing, can only be seen in low-grade, black-and-white footage, but the image of the crucifixes can be found in a split second when the episode is "recapped" in fast forward later in the show. Now available in full color.
In the narration to one Gilliam animation they crudely replaced the word "cancer" with "gangrene".
In the "Summarize Proust Competition" where Chapman's character was supposed to give his hobbies as "strangling animals, golf and masturbating", they muted the word "masturbating", leaving a very conspicuous silence followed by a big laugh. As Terry Jones later remarked, it's odd to think that strangling animals is all right but masturbating isn't.
A slightly better edit for later broadcasts and video releases re-dubbed the line as "Golf and strangling animals –" and cut out the next few frames to make it look like the host was ushering the contestant off the stage before he said anything even more offensive. Unfortunately the dubbing and cut were still quite obvious.
They would only allow the "Undertaker Sketch" to be recorded if some of the studio audience were seen protesting about it. Even so, the sketch was apparently cut from the master tape after transmission, and had to be reinserted from an NTSC copy.
The "Quiz Show"/"Spot the Brain Cell" sketch was cut from BBC repeats for several years, but restored for DVD release.
Some of the BBC's complaints stretched into downright paranoia. In the "New Brain from Curry's" sketch, a representative for the brain's delivery asks a Pepperpot to sign a fake leg; when the Pythons submitted the sketch for review, they were told to "cut the penis." The angle that Cleese held the leg into the doorway caused it to resemble an oversized Johnson.
The infamous "Wee-wee" sketch is one of only two filmed sketchesnote The other, one about an artist that makes a statue of Cleese only to give it an incredibly long nose, was cut for unknown reasons that have not only never aired but also failed to surface from the vaults. It revolved around a wine connoisseur being served urine by a French waiter and repeatedly believing he's drinking fine wine ("No, sir, zat is wee-wee."). The BBC didn't like it because one of the wine glasses was slightly rosé (pink), which they took to mean menstrual urine. Eric Idle protested, but the excuse was good enough for John Cleese who detested this sort of humor and managed to get the sketch canned for good.
In 1975, ABC got the rights to the Cleese-less fourth series, which hadn't yet been aired in the U.S. They planned to show them as two late-night specials, after they'd been cut for time and censored for content. The Pythons were horrified and tried unsuccessfully to try and block the broadcasts. But they did get a decision to allow their lawsuit over misuse of their material (on the grounds that the ABC version was inferior product under the Python name) to proceed. They settled out of court, with the Pythons winning full rights to the show.
Fake American: Many cases, to varying success. Even Terry Gilliam, who is American, had trouble sounding like it. For specific examples...
In the Marriage Counselor sketch, John Cleese plays a random cowboy with a laughably thick accent to help give a pep talk.
Bicycle Repairman has everyone attempting American accents, though a dead giveaway is when Cleese uses the word spanner instead of wrench.
John Cleese's narration in the Science Fiction Sketch goes an over-the-top Hollywood-style narration.
The Twentieth Century Vole sketch casts the entire group as Hollywood film execs.
The Attila The Hun show is done in typical American 50s sitcom fashion.
Fake Australian: The Pythons have also done this from time to time, including in "The Bruce Sketch", which features a bunch of characters all named Bruce, who are all teachers in the Philosophy Department of the University of Wallamaloo.
Magnum Opus Dissonance: John Cleese has often expressed frustration over the fact that, of all the high-minded, satirical sketches they'd done, it's the "Ministry Of Silly Walks," the one skit that deliberately made absolutely no sense, is considered their best (this also probably has to do with people stopping him the street and asking him to do a silly walk).
The Other Darrin: A couple of times one of the actors was needed to play another character, and was replaced mid-sketch once their lines ran out:
In "Court Charades", the jury foreman (Palin) and the defendant (Jones) were also two members of the Spanish Inquisition. When the defendant says "I wasn't expecting the Spanish Inquisition", the scene cuts to film of the Inquisition racing to the court house, and then cuts back to the studio when the Spanish Inquisition storms in; by which time the defendant has been replaced, and the foreman seems to have disappeared altogether.
In the "Father-In-Law" sketch, the father is played by Graham Chapman; when the sketch comes back as a link, he is replaced by Terry Gilliam.
On live stage productions, Eric Idle would sing the Lumberjack Song instead of Michael Palin.
Reality Subtext: "Spam" wasn't just an Inherently Funny Word that the Pythons thought sounded funny when repeated ad nauseam. Post-World War II England had a massive surplus of canned goods which they were still in the process of getting rid of some fifteen years later, so a restaurant trying to push spam onto a customer in a meal which didn't typically include it wasn't all that absurd (though it's safe to assume that few of these restaurants also served vikings).
Throw It In: During a sketch with John Cleese where they played a pair of Pepperpots, Graham Chapman suddenly went off script and screamed "BURMA!" for no reason. Cleese then asked Chapman, in character, why he did that, to which Chapman replied, in character, "I panicked!". It was later decided it was too funny not to include.
Cleese also described their writing process as extremely loose and fluid, never knowing where ideas would come from. For instance, the Cheese Shop sketch was born out of an idea of someone asking for cheese in a chemist's shop, until they asked "Why would he ask for cheese in a chemist's shop?" and the answer was "Well, he went to a cheese shop and they didn't have any."
Unfinished Episode: A sketch John Cleese found in poor taste was written but not filmed. (There is actually some controversy amongst the Pythons themselves as to whether it was filmed or not, but certainly never broadcast.) It involved a wine connoisseur showing off his wine cellar to a visitor, and after each tasting he reveals that it's "wee wee."