Woody Allen appeared on The Dick Cavett Show on October 20, 1971. These clips are from the Cavett "comic legends" DVD which I haven't seen, and are probably out of order.
In this one, Woody discusses the upcoming shooting of Play it Again, Sam and the writing of Everything You Always Wanted to Know About Sex. "I like my movies to be sloppy." But he likes his writing "to be "perfect." Talks about whether movies are art or not. Names three artistic films that rank with any other art form: The Seventh Seal, L'Avventura, and an Andy Hardy film, which gets a laugh. Cavett says that when he asked Welles the same thing, he answered Grand Illusion. It's a bit astounding that people had this conversation as recently as the 1970s, fifty years after the European avant-gardes of the 1920s and in the heyday of auteurism.
In one segment, Woody plays clarinet, bluesy, for laughs. It's so gratifying now to watch him please an audience. Then after a commercial he plays seriously and passionately.
Dick and Woody talk about food and health offers a kind of diet humor that seems totally unfunny now. Woody knocks over a table, then talks about avoiding cholesterol. Reminds me of the scene in Annie Hall when Alvy, out in L.A., orders a bowl of mashed yeast.
"Dick and Woody Debate Particle Physics" is the continuation of the last segment. Woody: "I would marry again, I think..." Yikes. Dick asks if Woody has a type. "I like pretty girls...and earthy looking...straggly earth mother sexual kind of animal disgusting types..." Then after the commercial: "My ex-wife is suing me because I made an amusing comment about her." This part is offensive by today's standards, which makes it all the more delightful as an object of nostalgia. Near the end Woody describes visiting Freud's house in Vienna.
The next clip picks up with Woody's discussion of his thirteen years of Freudian analysis, real intimate stuff. And a clip from Bananas. And Woody talks about being a college dropout, having failed out of NYU's motion picture production program and then City College's.
Then Woody plugs Getting Even. Lots of casual sexism in this one.
Groucho Marx in 1969 singing "Lydia the Tattooed Lady." His lascivious eyes didn't suffer with the passage of time.
Mel Brooks is introduced as "one of the world's weirdest men." He discusses his Oscar, his mother, his wife; does a bit of his borscht belt act (they call the Catskills "the mountains"), and around 5:30 does a little Man of a Thousand Faces. In another clip after the commercial break, Mel calls Dick an "extravagant Gentile" and does bizarre impressions: Humphrey Bogart's sister, James Cagney's Aunt Hilda. Then he sings an impression of Sinatra doing "America the Beautiful" which is as good as it gets (just the song part is here).
John Lennon and Yoko Ono is quite odd. Cavett speaks Japanese, Lennon speaks Yiddish. That's chapter 2 of the DVD. Another clip offers the true story behind "Lucy in the Sky with Diamonds" and "Happiness is a Warm Gun." Yoko doesn't talk a whole lot. In another episode, John discusses the origins of "Woman is the Nigger of the World," and he and Yoko perform it with their band. You can find other segments if you poke around.
Cavett interviewed by Charlie Rose in 2001. At 12:41 they roll a clip of a very young Cavett doing The Ed Sullivan Show. At 16:45 he talks about why he loved Groucho and then we get a clip of Groucho being interviewed on Cavett's show. 20:38 brings a clip of Katherine Hepburn talking about not wanting to be interviewed on a talk show. Around 24 minutes Cavett starts talking about stalking Greta Garbo. At 29:20, a clip of Gore Vidal and Norman Mailer being nasty to one another with New Yorker writer Janet Flanner and Cavett in the middle. Flanner blows Mailer a sarcastic kiss around 31:05 and Cavett starts to laugh one of those genuine private laughs you don't often see on talk shows. Then Mailer calls the other three "intellectually smaller" than himself! What a shmuck! He patronizingly tells Cavett to ask the next question on his question sheet, and Cavett comes back with a perfect line: "why don't you fold it five ways and stick it where the moon don't shine."