Revealing mistake: In the scenes in the cockpit, when Kareem Abdul-Jabbar (Murdoch) is talking, you can see his eyes move back and forth like he's reading from a cue-card.
Revealing mistake: When the doctor is removing the eggs from the woman's mouth, he actually has them in his hand, not taking them out of her mouth. A simple sleight of hand, but still noticeable.
Answer: This is a reference to The Godfather, where a character being intimidated by the Mafia wakes up with his prize racehorse's severed head next to him on the bed. For comedy purposes this is twisted by the movie as an implied sexual relationship, when the horse is revealed to be alive.