Michael Palin's father stuttered, so Palin used a lot of his real-life experience when playing Ken Pile, including the fact that Ken's stutter is less pronounced around people he trusts (George Thomason and Wanda Gershwitz) and worse around people with whom he is uncomfortable (Otto West).
Actor, executive producer, and writer John Cleese chose the name "Archie Leach", Cary Grant's real name, because he was born twenty miles away from where Grant was born (Hughenden Road, Horfield, Bristol, England), and because it was the closest Cleese could get to being Grant.
Jamie Lee Curtis was listed as "Jamie Lee Schwartz" on all of the call sheets, because John Cleese found it amusing that her father Tony Curtis' real name was Bernard Schwartz.
Jamie Lee Curtis buried her face in pillows during Kevin Kline's ejaculation scene, to keep her from bursting out laughing at the faces he was making.