The title of the episode is a parody of a television series called Love, American Style that ran from 1969 to 1974.
The first segment is a retelling of Bonnie and Clyde, and the characters in the cartoon of this segment are parodies of Woody Woodpecker and Speedy Gonzales, which Chief Wiggum finds racist (a reference to how modern audiences feel about such ethnic cartoon characters as Speedy Gonzales).
The second segment of the episode is a parody of Lady and the Tramp. The dog taken into the gas chamber in "Shady and the Vamp" is a parody of Disney's character Goofy.
The third segment is a reference to the romance of Sid Vicious and Nancy Spungen and the film Sid and Nancy. Bart is also featured in the story as Johnny Rotten. The plot has chocolate substituting drugs which is similar to the Season 15 episode, "The Regina Monologues". CBGB was a music bar (though here we discover that it stands for Comic Book Guy's Bar).
Although a Sex Pistols song was featured in "Missionary: Impossible" ("No Feelings" during the "Do Shut Up" sequence), the Pistols in the Sid and Nancy sequence do not actually sing any Pistols songs.
Ironically, Both real love stories in this episode ended up tragically. Bonnie and Clyde were ambushed in 1934, as shown in the episode, and Sid Vicious murdered Nancy Spungen in 1978 and possibly commited suicide years later. Shady and The Vamp is based in The Lady and The Tramp, which is a fictional story.
Nancy was not a model student when she met Sid Vicious. She was actually a rebelious teenager that ran away from home and moved to New York, meeting him on a show.
Paul Cock (Dolph) refers to Sid Vicious as Sidney Sheldon Vicious, but his real name was John Simon Ritchie.
This is the first episode in a row where a character (Bart/Nancy) orders another character to do something (Skinner to go knitting/Sid to bang his head against a wall) and they obey, claiming they're only doing it because they want to.
In the second segment Vamp the Lady version, is blue unlike the movie where she is tannish. Also her collar is red instead of blue.
Vamp doesn't go to the pound unlike the puppies. Also in the movie Lady was in the pound wearing her license and wasn't going to be put to sleep.
Vamp has 11 puppies unlike the movie when Lady has only 4: Annette, Danielle, Coliette, and Scamp. They are 3 girls and a boy.
Also in the segment Shady doesn't have many girlfriends only Vamp. But in the movie Tramp has about 7 or 8 girlfriends before Lady including: Lulu, Trixie, Fifi, Rosetta, Sequita, Sewawa (or Pedro thinks that Rosetta, Sequita, and Sewawa were his girlfriends) and Peg (implied). Its implied they are strays as Tony said that Tramp should settle down with Lady.
The Selma and Patty siamese cats seem to live with Vamp in this segment. However in the movie they only appear as Aunt Sarah's cats as she is in charge of Lady, the house, and the baby while Jim and Darling go on a trip.
Jock and Trusty dogs appear as Shady's friends unlike Lady's. However the dogs in this segment aren't wearing collars making them indeed strays.
The Moe dog that looks like Bull is black instead of Bull's lightest brown.
A Peg dog doesn't appear in the pound. It only appears as an Edna like dog and only for less than a second.
There aren't any humans in the segment possibly to maintain the dog's persective.
The Moe dog doesn't appear in the pound as in the movie Bull is in the same cage with Lady, Peg, Boris, Pedro, and an unnamed dog.
The spaghetti scene is parodic but instead of them kissing through a noodle, Vamp's head gets sucked up into Shady's body.
There are about 5 other type of animals eating dinner at the restaurant while in the movie only Lady and Tramp only have the dinner as Lady is a Cocker Spaniel and not a stray.