Fake Nationality: Almost completely averted. John Banner was Austrian, the rest of the cast matched the nationality of their characters. Major Hochstetter — a character not in the main cast — was played by an American actor.
The series has a shared reality with Green Acres. During a flashback from Oliver's World War II years, both Colonel Hogan and Stalag 13 are mentioned. Colonel Klink also showed up in — of all places! — the Batman TV show and The Simpsons.