Johnny Fever's line, "Badges! We don't need no stinkin' badges!" is taken from The Treasure of the Sierra Madre (1948). It is often misquoted in films and TV.
When they are posing for the swimsuit photo shoot, Andy refers to Jennifer as "Annette". He is referring to Annette Funicello, who stars in the Beach Party (1963) series of movies. It is also a play on words on Andy's name.