Acceptable Religious Targets: Just about everyone, including non-religious people. Most frequently mocks the Church of England. The only known exception is a sketch involving a radical Muslim Caliph originally slated for Monty Python's The Meaning of Life which was later removed. (Cleese is particularly thankful for that, considering he claims it would have resulted in a fatwah put upon the Pythons.)
Terry Gilliam played a nude organist for the "Blackmail" sketch, a full season before Terry Jones' crazy haired version.
Graham Chapman's colonel who complained about things getting too silly was preceded by Graham Chapman's colonel who complained about copyright violations of the British Army's slogan "It's a dog's— pig's— man's life, in the modern army". The transition came in the episode "Full Frontal Nudity", where the Colonel begins a sketch in his first role — admonishing a soldier who thought from the British Army's recruitment campaign it was all about water-skiing and other adventures rather than killing — and then breaks the fourth wall with "Stop that, it's silly" when the sketch turns into a gag about two Mafia men intimidating him for menaces money. He then reappears throughout that episode (and ever afterward) to stop sketches he considers silly, and the earlier characterization was abandoned.
Certain sketches fall under this as well. The Four Yorkshiremen sketch was originally written and performed for At Last The 1948 Show, but the Pythons (two of whom, Chapman and Cleese, had been a part of said show) began performing it in their live stage shows, including on Monty Python Live at Drury Lane and Monty Python Live at the Hollywood Bowl leading to its association with the Flying Circus. The "Job Interview" sketch had originally been written by Cleese as part of a 1968 American television special, How To Irritate People (also featuring Chapman and Palin); Cleese's 1948 co-star Tim Brooke-Taylor played Chapman's interviewee role. It's worth noting the same special also introduced us to the Pepperpots.
Some people don't even know there was a TV show, knowing the Pythons from the movies.
Bizarro Episode: Inverted. Out of four seasons' worth of loony, schizophrenic episodes, only three of them - Series 3's "The Cycling Tour" and Series 4's "Michael Ellis" and "Mr. Neutron" - have a linear plot that's generally adhered to from the beginning of the show to the end.
Crosses the Line Twice: Many times, most notably with two sketches involving cannibalism. The BBC only agreed to air the infamous "Undertaker" sketch was if the audience stormed the stage at the end.
"Never Be Rude To An Arab".
In case the name didn't tip you off, the "Mr and Mrs Niggerbaiter" sketch.
Discredited Meme: The jokes have been quoted so many times that it's become a joke to repeat the jokes.
"The Mouse Problem" satirized then current attitudes of homosexuality by replacing homosexuals with men who dress up like mice; today, we now have fursuiters.
"The Cycling Tour," starring Michael Palin parodies presciently the same travelogues he would be famous for decades later.
Also the Whicker's World parody. Palin's first travelogue series, Around The World in 80 Days, was originally intended for Alan Whicker.
In "The Science Fiction Sketch", they mention how Scotland is the worst tennis-playing nation on Earth, but a Scotsman saves the day by winning Wimbledon. In 2013, Scotsman Andy Murray won Wimbledon. The same sketch features a Mr. and Mrs.Harold Potter.
The "Poet McTeagle" sketch featured a poet who did nothing but beg for money. Now we have Kickstarter, which is essentially creative people begging for money.
The "Germany vs. Greece Football Match" ends with Socrates realizing that the philosophers are in a football match, dribbling the ball to Germany's goal, and scoring the only goal in the match. Later, in the 1980s, there was a player on the Brazilian World Cup team named Socrates.
The idea of the "Wee-wee Wines" sketch i.e. urine being passed off as fancy wine, was nixed by either BBC management or John Cleese, depending on who you ask. This exact joke finally was aired in the Blackadder II episode "Potato".
During the "Court Scene (Charades)" sketch in Episode 15 ("The Spanish Inquisition"), John Cleese as the QC (i.e. prosecutor) mistakenly calls for Exhibit Q. In 2002, Cleese would play the character Q in the 007 film Die Another Day.
One of the subsidiaries of Confuse-A-Cat Ltd. is called "Bewilderebeest" - a term that means something very different to How to Train Your Dragon 2 fans than the simple act of bewildering a wildebeest.
In the "Communist Quiz" sketch, the quizmaster asks Che Guevara when Coventry City last won the FA Cup, and then throws the question to the rest of the panel. When no-one answers (Communist philosophers and politicians not having much time to follow English football), he reveals that it was a trick question: Coventry City have never won the FA Cup. The sketch aired in 1970; in 1987, Coventry City won the FA Cup, making re-runs of the sketch highly amusing to Sky Blues fans.note In the same sketch, Mao Zedong surprises all present by knowing that Teddy Johnson and Pearl Carr's 1959 Eurovision Song Contest winner was called "Sing Little Birdie". However, that song finished second; the winning song was the Netherlands' entry, "Een Beetje" ("A Little Bit") as sung by Teddy Scholten.
After poor Arthur 'Two Sheds' Jackson is kicked off of the set by his interviewer and an interviewer from a previous sketch, the linkman is interrupted by this conversation from off screen:
Third Interviewer: Never mind, Timmy.
Second Interviewer: Oh, Michael, you're such a comfort.
During "The Visitors", you have Mr Freight, the extremely Camp Gay man who has brought along Mr Cook, who he has 'picked up outside the Odeon'. He spends the rest of the sketch with his arm around Cook, and kisses his cheek twice. Cook repays the favour by stroking Freight's chest.
This often happens whenever a Python in drag (usually Terry Jones) starts flirting with another Python who isn't in drag. The best example of this is during the "Poets" sketch, wherein Terry, dressed as a woman, flirts openly with Michael, makes comments about his torch and ends up lying on top of him, their faces inches apart.
Informed Wrongness: The narrator of the "Mr. Neutron" sketch keeps telling us that Mr. Neutron is plotting to destroy the world, yet we never see Mr. Neutron do anything even remotely evil, except flirting with a married woman, and is a pretty nice (if odd) guy.
Lowest Common Denominator: In "Njorl's Saga", there is a TV executive put on trial and defending himself by saying that television is all about popularity, and that the average viewer wants entertainment, not 3 hours of documentaries.
Exceutive: Quite frankly, I'm sick and tired of being accused of being ratings conscious.
The Pythons were dismayed that people were looking for deeper satirical meaning in the "Ministry of Silly Walks", which they said was just a silly sketch; John Cleese focused on fans who thought the sketch was their best.
The opposite happened with Monty Python's Life of Brian, where the Pythons really were parodying the divisions in Britain's left-wing parties.
Seasonal Rot: The fourth and final series is widely considered to be the weakest one. The Pythons themselves share this viewpoint; John Cleese, having become tired with the show, had left after the previous series and they agree that without both his contributions and his quality control things were getting a bit weaker.
Seinfeld Is Unfunny: Hearing people recite their favorite sketches for the 16,047th time can be aggravating, to say the least - especially since the creator's aim was to make a show that is completely unpredictable.
Their "Spanish Inquisition" sketch has become such a classic that it's now easy to forget what made it so funny the first time it showed up: it was (hence their catchphrase) completely unexpected, with the Inquisition barging into an unrelated sketch without warning. Needless to say, watching it in a YouTube video titled "The Spanish Inquisition" spoils the joke just a bit. One wonders why the people uploading such videos don't retitle them, "Trouble at t'Mill", and "Pictures of Uncle Ted" to avoid this.
John Cleese remembers performing the "Dead Parrot Sketch" live, and, as a laugh, Michael Palin changed the script in order to try to get Cleese to start Corpsing. He succeeded (rather than, when asked if a slug can talk, answering "not really", he said "well, it mutters a bit"), and Cleese laughed so hard he forgot where they were. He asked the audience, all of whom shouted the next lines back at him, making him think "what's the point?"
Special Effect Failure: "Salad Days" features several, such as John Cleese's "hands" being blatantly severed before the piano gets smashed on them, and the woman whose head is knocked off by a piano keyboard clearly being a mannequin. This only adds to the humor, and was probably intentional (in addition, there were obviously budget constraints as well).
Values Dissonance: All things considered, the Pythons' portrayal of female, gay, and non-white characters is often rather offensive when viewed today. Obviously Grandfather Clause and Rule of Funny liberally apply — as does the fact that one of the Pythons, Graham Chapman, was himself gay — but for first time viewers, the dissonance can be jarring.
What an Idiot: In the "Election Night Sketch", the unofficial "Very-Silly Candidate" gets two votes (presumably from people who would've voted for the official Silly Party Candidate), thus allowing the Sensible Party to take the constituency by a single vote. Also, the Slightly-Silly candidate gets zero votes, indicating that he didn't even vote for himself.
What Do You Mean, It Wasn't Made on Drugs?: Word of God insists unanimously that it wasn't. Their sketches may look spur-of-the-moment, but they were actually very tightly written, often depended on split-second timing, and hence were well-rehearsed — they actually wouldn't have been able to produce the show had they been under the influence (their frustration with Chapman's alcoholism still emerges in reminiscences forty-odd years later). Of course, what they may have got up to in their leisure hours was something else again...