Dan Aykroyd took his daughter, Danielle Aykroyd, to see the film being made, and she was so fascinated by the Conehead costumes she asked for one of her own. She was cast as Connie at age three so she could get her own cone.
Toward the end when Beldar asks Ronnie if he could have fifty-five words with him, he does, in fact, say fifty-five words.
The French representatives of UIP took great exception to the Coneheads disguising their extra-terrestrial origins by passing themselves off as being French, and insisted that all such mentions be removed from the dialogue. This demand was declined.
The shiny card with the alien symbols on it that Michael McKean's character finds in the Coneheads' trailer is a diagram showing the escape routes out of a Conehead craft in the event of an emergency landing.