Carrie asks Doug if he knows who was President of the United States when Arthur was born. The answer is Calvin Coolidge, who was in fact also POTUS at the time of Jerry Stiller's birth.
One of the guests (played by Orson Bean) at Arthur's surprise birthday party is accused of sleeping with another guest's wife. 5.25 years later on fellow CBS sitcom Two and a Half Men (2003), Orson Bean plays a character who accuses title character Charlie Harper of sleeping with his wife.
After Carrie and Arthur get back home, he tells her that he'd like everyone at the party to surprise him by singing "For He's A Jolly Good Fellow." In Godfather Part 2 (1974), the Corleone family sings Vito Corleone the same song after surprising him for his birthday.