The Warner Siblings are infamous for nearly always playing the role of the retaliator in their cartoons and getting the better of their victim...except for when they meet someone astoundingly dull, resulting in them expending all their energies in a desperate attempt to get away from them.
From "Hooked on a Ceiling": An enraged Michelangelo hits a nearby column with his fist, which causes it to crumble and reveal his famous Horned Moses statue. You might not realize it, but it's an obvious reference to his belief that statues were "trapped" in every stone block, and that the sculptor's job was to reveal, rather than create them.
I noticed something about some of the educational songs and the tunes used for them. "Yakko's World" is sung to the "Mexican Hat Dance," which would be a song that the American viewers would associate with a foreign country (although a specific one). "Wakko's America" is sung to "Turkey in the Straw," which is a traditional American folk song that would be suited for a song that is specifically about American states. The song "Yippie-Ki-Yi-Yo" is about a rancher traveling with his cows, and it is used for the song about Magellan's voyage. Finally, the song about food ingredients is to the tune of the Can-Can, which is commonly associated with France, which is also famous for its food.
Pretty much any time drums are required (for instance, in "Little Drummer Warners" and whenever there's a Rimshot gag), Wakko is the one who plays them. He is based on Ringo Starr.
We all remember the episode "Meatballs or consequences", where the Warners annoy Death himself. But what's interesting is that the fact that he would be together with the Warners drove Death over the edge. Thus, confirming that being with the Warners is A Fate Worse Than Death.
The Warner siblings are sometimes referred to as the Warner Brothers and their sister Dot. A dot follows the words "Warner Bros" on the Warner Bros. logo, as seen here.
Mindy only ever calls her mother "lady", despite her mother insisting to be called "Mom". Considering that she only leaves Buttons in charge of watching Mindy, and never does it herself, Mindy probably doesn't think she's a good parent.
Skippy is eaten up by the death of Bumby's mom. Considering he lives with his aunt, his parents are never mentioned, and there was an episode where CPS takes him away, it's possible his parents died and the movie struck a chord with him.