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.
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.
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. The Blue-Haired Lawyer is very nitpicking with imitations and retellings.
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.
Grampa shouldn't get gas bills, since he lives in a Retirement Home. The Retirement Castle is so cheap, it would be no surprise if they made the residents pay all of the bills!
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.
Grampa plays the organ at the wedding where Burns and Jackie are nearly married. How did he get up to that little room with the organ? There is no door leading into or out of the "organ room", and a sheet of glass in front of the "front" of it. Additionally, the "organ room" was not there in any previous episode. This was most likely intended as a one-time gag and not meant to be taken too seriously, though.