The Black Knight getting dismembered. John Cleese admitted as much in his commentary track. He explained that some viewers in America found the sequence horrifying because of Vietnam War footage on the news; however, he noted that they began to laugh when BK's first leg got hacked off and he was still raring to go.
Lancelot's "rescue" in which he charges into the castle and slaughters half of the townspeople under the belief that they're kidnappers. The heroic music and the fact that he turns his wrath on not only guards and peasants but the bridesmaids, the wedding band, and a torch on the wall make something that should by all rights be horrifying absolutely hilarious.
Discredited Meme: The constant use of quotations from it has caused it to become popular to mock people for quoting it so much.
Ear Worm: The drawbar organ music during the "intermission" and at the end.
Ensemble Darkhorse: The Black Knight, despite only being in one scene, is arguably the most famous character in the film.
The Black Knight and Lancelot are played by the same person (John Cleese). And then, in Fate/Zero... Lancelot IS Black Knight/Berserker.
A few years after the film came out, Jimmy Carter was attacked by a rabbit.
In Monty Python's Life of Brian, Brian uses his (Chapman's) prominent Roman nose as proof that he is part Roman. Arthur, also portrayed by Chapman, is historically said to have been Romano-British. Incidentally, Chapman also played Raymond Luxury Yacht (It's pronounced Throat Warbler Mangrove!) in the series, who appears on set with a huge fake nose.
It has been suggested with complete seriousness that coconuts really did migrate naturally. The claim is heavily disputed, but just being plausible is hilarious even if it's not true.
Memetic Mutation: Essentially, the whole film. There's not one scene that isn't eminently quotable, and several exchanges are considered required basic knowledge for nerd cred.
Nausea Fuel: First-time viewers or the very squeamish may find the Black Knight scene to be more off-putting than intended, due to the copious amounts of blood and Body Horror.
One-Scene Wonder: The Black Knight and the killer rabbit are well known and well quoted despite having little screen time.
Seinfeld Is Unfunny: The best jokes from this movie have been memes for so long and are so familiar by now that it might not be clear why they were ever really funny in context. In fact, quoting the movie around LARP groups is often strictly frowned upon, especially if it's a newcomer to the group who has never done a LARP before. Not only because they've all heard those references before, but because if one person starts doing it, everyone will start doing it.
Signature Scene: The fight between Arthur and the Black Knight is the most well-known and widely-quoted scene in the entire film. And possibly of the Monty Python franchise as a whole.
It's revealed in the DVD commentary that the dye used on the Rabbit's fur didn't wash out, causing the cast to be quite embarrassed when the owner showed up (having been promised this wouldn't happen).
It can be very hard to take Arthurian legend seriously after seeing this movie. There have also been reports of audiences bursting into laughter during violent sequences in movies like Excalibur.
Quoting The Holy Grail has become such a tradition among Dungeons & Dragons tabletop due to its close association with Medieval Fantasy, that most newcomers become well immersed in the film's jokes before they've even seen it, and are likely introduced to it through tabletop.
As noted under Seinfeld Is Unfunny above, it's become so prevalent that many groups actively discourage quoting the film. Not only because everyone has already heard it, but because once one person starts in, it's inevitable that the entire group will soon be doing it.