Steve Zissou is based on Jacques-Yves Cousteau. Cousteau's famous ship was called Calypso. Harry Belafonte became famous singing calypso songs, and his record Calypso (1952) was number one on U.S. music charts for 31 weeks.
A quote from Cousteau is featured in Rushmore.
Jane Winslett-Richardson is modelled on the primatologist Jane Goodall. The name was inspired by Kate Winslet.
Drakoulias' glasses are based on those of Italian film director Sergio Leone.
The likeness of Jacques Henri Lartigue, whose work inspired one of the photoshoots for Rushmore, was the basis for the portrait of Lord Mandrake.
The "I'm a Pepper" t-shirt worn by Alistair Hennessey also appears in the Bottle Rocket short. One of the Fillipino pirates is wearing a hat from Wes Anderson's alma mater, the University of Texas.
Seu Jorge's name in the film, Pelé dos Santos, appears to be a play on the name of the famous Brazilian soccer player, Pelé (Edson Arantes do Nascimento), and his team from 1956-1974, the Santos Futebol Club.
The Zissou flag is inspired by those featured in the classic Kurosawa film, Seven Samurai (1954).
The end sequence is inspired by The Adventures of Buckaroo Banzai Across the Eighth Dimension (1984). Like in Banzai, a dead character (Ned Plimpton, smoking a pipe), returns. Peter Bogdanovich did a similar "curtain call" in The Last Picture Show (1971).
"Not this one, Klaus" (Zissou) is a reference to Jules and Jim (1962).
The "Mutiny on the Belafonte" scene was inspired by Fitzcarraldo (1982).
The space suit in the Adventurers' Club is from Mission to Mars (2000).
Some of this information was researched by the soundtracks blog, The Playlist.