The title is a reference to the 1960s sitcom My Three Sons.
The "Essence of Elzar" television show and the Elzar character parody the 20th century Essence of Emeril show and its host chef.
As Bender goes through the robot wash the song, "Car Wash" by Rose Royce plays. Also, Bender sings his own version.
Head Shop: slang for a shop where drug paraphernalia for potheads is sold. In/on Little Neptune, the "Head Shop" sells human heads.
Bender cooks wearing a chef's apron bearing the bold text "TO SERVE MAN". This is a reference to a Twilight Zone episode based on the short story by Damon Knight, both with that title. In that story, the large book carried by giant aliens promising a bright future for Earth and its inhabitants turns out to be a cookbook. The premise of this pun is the same as the Moebius underground comic strip Is Man Good?.
The Galaxy of Terror is a reference to a low-budget 1981 sci-fi movie Forbidden Zone, and an area in the Planet of the Apes movies.
In the Little Neptune Market, when Bender is looking through the shop glass, there's a parody of the "I Can't Believe It's Not Butter" advertisements which reads "I Can't Believe It's Not Slug".
One of Bender's prime minister's sash medals features an image of Homer Simpson. Also, there is a badge with a "Arm and Hammer" style emblem, which is an arm with a rolling pin, stating that he is/was the ship's chef.
The Alienese sign behind the Emperor's Bottle reads "Do not drink the Emperor".
