Season 25 is referenced indirectly by Homer asking Marge if she thinks their marriage will last 25 years to which Bart slyly replies to the camera "Nothing should".
The scene in which Bart and Lisa play pillow fight and accidentally break a lampshade contains some references to communism:
After the lampshade is broken, Bart says that "Lisa has made him break the lampshade": this refers to Vladimir Lenin's ideologic strategy of "accusing your enemies of doing the things that you do, calling your enemies the things that you are", which is a regular in communism;
Lisa retorts by saying that Bart "distorts the facts in an orwellian way", which alludes to George Orwell;
Marge complains that both kids never cease fighting and using obscure references, to which Lisa mentions Orwell's 1945 novel Animal Farm;
Bart whispers to Lisa that "grandpa says that Orwell was a communist".
Homer and Marge claim to be celebrating their tenth anniversary, even though they had their eleventh anniversary in "Natural Born Kissers". Also, if it's their tenth anniversary, this would make Bart a bastard. It has been stated many times that he isn't.
Bart calls Homer "Daddy" as a baby despite that in "Lisa's First Word", he always called him "Homer" at age 2.
The flashback at the episode start shows Bart as being older than Nelson, which is inconsistent with the entire series timeline.
The flashback at the episode start shows Jeremy Freedman was a teenager almost nine years earlier, however he should have appeared as an elementary school boy. "Lard of the Dance" implies that he is not the only Squeaky Voiced Teen in Springfield; it's possible there were many before him.