The chip can Andy holds is a parody of Pringles right down to the mascot.
Andy Hamilton is the name of a British television and radio comedy writer, co-creator of Drop the Dead Donkey (1990).
Bart tells a member of Krusty's backstage crew that Andy is going to ruin the show, and the crewman quips, "Ehh, he's about 20 seasons too late!" This episode is from Season 21.
The classical music heard, the Troika from Lieutenant Kijé by Sergei Prokofiev, was also used in Woody Allen's classic comedy Love and Death (1975).