The Diva Plavalaguna's name was used as an inside joke referencing Milla Jovovich's second film, "Return to Blue Lagoon" (plava laguna means "blue lagoon" in Serbo-Croatian).
Luc Besson thought about the story when he was in high school.
In the movie, the bizarre Divine Language that Leeloo speaks was invented by Milla Jovovich and director Luc Besson. Milla Jovovich is multi-lingual, and by the end of filming the movie, the two of them had learned to speak it fluently, even engaging in full conversations in the language.
Interesting and fun to watch for: As a visual representation of their exact opposites, Zorg usually has a large circle behind him, whereas Korben usually has a large rectangle behind him during important scenes involving major decisions by their characters.
When the shuttle leaves Earth to go to Fhloston Paradise, the flashes behind the shuttle have the same shape as Gaumont's logo. Gaumont is the company that produced this film.
The real name of one of the policeman that is waiting in front of the McDonalds is Mac Macdonald.
When composer Éric Serra showed Inva Mula, the Albanian soprano who was going to sing the Diva Dance, the sheet music for that part, apparently she laughed and said that it was impossible for the human voice to switch from high to low notes that quickly. She got her way: The part that ended up in the film is not a single piece of audio, rather it's several pieces stitched meticulously together.
When Leeloo is fleeing from the cops and is startled by the elevator that goes down past her, on the roof of a grey bus passing along side it, you can see "KG62" written on it. "KG" are Karen Goulekas' initials, the film's digital effects supervisor, and "62" is her birth year. This is confirmed on the DVD's visual effects commentary.
At first, the film was supposed to be filmed in France but there were no studios big enough so they had to transfer the production to London.
During the opening credits, when the Earth rotates from the bottom of the screen to the left, listen carefully to the music. It is the same music played just after the Klingon ship goes back in time to 1986 in Star Trek IV: The Voyage Home (right after the heads of the Enterprise crew morph on screen).
Zorg's desk and the accident with the cherry is a reference to the film Tintin and the Lake of Sharks, where Rastapopoulos has the same kind of problem.