Dennis the Menace — Jay North reprises his role as the title character of the 1959-1963 sitcom at Greaser's grand opening. (Bart was originally conceived by Matt Groening to be a more extreme, and truly menacing, version of Dennis.)
Wolfman Jack and Debbie Dunham — Restaurant proprietor Wolfguy Jack and his girlfriend are thinly veiled caricatures of the radio personality and the character from American Graffiti, respectively.
The episode title is a pun on the classic Henny Youngman one-liner, "Take my wife, please."
American Gothic — The painting featuring Apu and Manjula standing in front of the Kwik-E-Mart is based on Grant Wood's famous painting. (The farmer in Wood's painting is holding a pitchfork, but Apu is holding a broom.)
Friday the 13th — The Hell's Satans are staying at Camp Crystal Lake, which is named after the campground where Jason Voorhees terrorized teen-agers in the slasher film series.
The bike Homer wins is a 1955 Harley Davidson FLH Panhea
The name that Homer gave to his Biker group, as well as the actual group of the same name that menaced Homer afterwards, Hell's Satans, were a spoof on the real-life biker group Hell's Angels.
"Hell's Angels" — In the scene where the real Hell's Satans take over the Simpsons' living room, Hunter Thompson, author of the book Hell's Angels is seen briefly sitting by the back door. This is a reference to the fact that Thompson held parties in his apartment during the time of writing his book of which the Hell's Angels were frequent guests.
Homer's motorbike has training wheels you can actually get training wheels for a motorcycle.
Homer seems to send Marge back in time during the dance contest.
No wonder Greasers Cafe went out of business if they give away a prize like that for the dance contest, they have a Nightly dance contest.
When Homer is sitting at the table after the bikers leave the Simpsons' house, he raises his fork behind his head, and when he brings his hand back into view, the fork is on the table again.
In "The Homer They Fall", Homer was shown to be so weak, he couldn't even harm a fly with his punch, whereas in this episode, Homer can easily swing a motorcycle like a sword. However, he may have picked up some strength after that episode and before this one.