On IBN, there is on the bottom of screen a sign "Limited Edition 800.000" near pictures of Itchy and Scratchy.
The animation cell rolled in cardboard has DO NOT ROLL stamped on it.
Jacqueline mentions to Abe that in her youth she got all the attention from boys and it drove her best friends 'crazy'; she names said friends as Zelda Fitzgerald, Frances Farmer and Sylvia Plath, all of whom were famous women who later developed severe mental illnesses; Schizophrenia, Paranoid Schizophrenia and Clinical Depression respectively.
Maggie turns a year old in this episode (She used to be in her first eleven months for the first 101 episodes of the show, and for seasons 1-5), and has been a year old since this episode.
According to Lisa, Maggie apparently doesn't get along that well with kids her age--this was said after Bart questioned whether they should wait for the other babies to arrive before Maggie opened her birthday presents. Lisa was the one who pointed out that they didn't invite any other babies to the party (besides her, Bart, Homer and Marge, the only other people to attend the party were Abe, Jackie, Patty and Selma).
The ending of the episode with Grampa crashing the wedding is a spoof of the 1967 movie The Graduate.
The song "The Sound Of Grampa", played during the last scene and credits of the episode, is a parody cover of Simon and Garfunkel's "The Sound of Silence", which was played during the end scene and credits of The Graduate.
Grandpa performs the classical "roll dance" by putting bread on two forks and making it dance. The roll dance is from Charlie Chaplin's The Gold Rush. He's even almost arrested for "copying" Charlie Chaplin.
Abe's line "Goodnight Mrs. Bouvier, wherever you are" is a reference to Jimmy Durante's catchphrase.
The chalkboard gag is a reference to a copyright notice by Major League Baseball, warning everyone that it is copyright infringement to rebroadcast, retransmit or reproduce MLB programming without permission from MLB.
As the family welcomes Mr. Burns to their home, Burns call Maggie 'Pebbles', and as Homer takes the chocolate he screams 'Yabba dabba doo!', in reference to The Flintstones.
Despite the claims of the Blue-haired Lawyer, Grandpa's imitation of Charlie Chaplin isn't violating any copyright law, as The Gold Rush has been in public domain since 1953.
When Bart looks through the mail slot, the delivery man with the animation cell has yellow skin, and is wearing a light brown shirt with dark brown pants. But when Bart steps out he has darker skin, and is wearing a blue jumpsuit. He still has the darker skin color when he punches Bart, but in the next shot he has yellow skin again.
Reverend Lovejoy begins his bible reading without a podium, even though his hands are extended before him as if he were resting them atop one. In the next shot, the podium is there in front of him.