Indecent Proposal - The film is punned in the title and referenced throughout the episode.
"Nookie in New York" is an obvious parody of Sex and the City, right down to the appearance of the characters. Patty's remark about how the four women "act like gay men" also referenced a common criticism of the show as well as how the writers originally intended for the female leads to actually be gay men. More specifically, Homer referenced that franchise in Trilogy of Error.
The point where Artie is flying Marge away in his helicopter, and Marge sees that Homer has written "KEEP YOUR CLOTHES ON" in rocks, is a parody of the series finale of M*A*S*H, Goodbye, Farewell and Amen, in which Capt. Hawkeye Pierce, as his helicopter takes off to fly him homeward, sees that Capt. B.J. Hunnicutt has written out the word "GOODBYE" in rocks.
At the end of the episode, Artie's Snor-Converter alters Homer's snoring into the tune of "Sweet Dreams (Are Made of This)" by the Eurythmics. Artie supplies altered lyrics where he tells Marge that Homer is a loser and she should dump him.
Moe says to Homer about Artie that "he's like a spy in the house of Moe". This could be a reference to the lyric "I'm a spy, in the house of love" from the song "The Spy" from The Doors.
When Homer says he won't be born if Marge marries Artie, it is a reference to Back to the Future: Part I, wherein if Lorraine doesn't marry George, Marty won't be born.
Comic Book Guy says in his sleep : "Oh, Jar Jar! Everyone hates you but me." This is a reference to how most people who watched the Star Wars prequel trilogy hate the character Jar Jar Binks.
That 70's Show - Homer saying "good day... I said good day" is a reference to Fez's catchphrase he uses when pressured.
Homer has a Funzo to illustrate Marge kissing Artie Ziff ("Grift of the Magi"). However it was purple with red hair and a blue ribbon, but when Bart got it, his Funzo was pink with blue hair and a green ribbon. Bart's Funzo was likely burned in the Tire Fire at the end of "Grift of the Magi".
It is possible Homer may have simulated snoring with his eyes open to get Marge to agree to the money for the surgery.
Homer and Marge can’t afford the surgery for Homer’s snoring from Dr. Hibbert, but they didn’t consider going to Dr. Nick Riviera, who could perform any surgery for only $129.95 in Homer’s Triple Bypass.