California Doubling: The Swedish town Tomelilla doubles for Madrid, Paris, London, and New York, among other places. In fact, there's one shot in every city that shows the same street from the same angle as a sort of Lampshade Hanging.
Culture Police: In America, Prohibition is not about alcohol, but art. Secret galleries work as speakeasies for people who want to see art, and are raided by the police; smugglers bring in paintings and sculpture from Canada, and Picasso gets a job producing, essentially, the art equivalent of moonshine for art-starved Americans.
Notably averted by Gertrude Stein and Alice B. Toklas, both played by British actors, and Grieg, the Norwegian electrician. Also semi-averted by Ingrid Svensson-Guggenheim, a Swedish-American woman played by a Swedish actress.
Fat and Skinny: Two background extras who appear together in many scenes.
Gainax Ending: The ending scene is pretty bizarre. It's even unclear whether Picasso dies or not.
Gratuitous Foreign Language: The Narrator speaks in Swedish, but the characters speak (often very broken) Spanish, French, English, German, Russian, Finnish and Norwegian. The things they say are regularly out of context, and it provides a lot of Bilingual Bonus if you understand what they are saying.
Historical-Domain Character: The film is full of these. It loosely follows Pablo Picasso's life, and a lot of his contemporaries also appear in the film, including artists like Braque, Matisse, Fernand Léger, Ernest Hemingway, Guillaume Apollinaire, Henri Rousseau, Vincent van Gogh and no less than two Toulouse-Lautrec, as well as political leaders like Adolf Hitler and Winston Churchill.
Hot-Blooded: Picasso's mother, appropriately for a Spanish lady.
Street Musician: Don José pretends to be a blind street musician after World War I. When he puts down his violin, it goes on playing the tune, then a close-up reveals that it is actually a wind-up music box.