Their contracts, which are a form of contract where the talent gets paid, whether or not the project is made. Now, remember, they were just thrown in the water tower, and nothing else was done with them, outside of a handful of cheap knock-off cartoons... and their contracts meant they were getting paid for the entire hiatus!
It's also a clever move on the part of the cast at large; the terms of the contract ensured each of the characters got paid for every episode, regardless of whether or not they appeared, accounting for the cast's rotating schedule. The characters took care of themselves, and the network executives got the short end of that one.
Those contracts can also explain why there were so many cameos—might as well make use of the talent if they're getting paid anyway.
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 - like Francis Pumphandle - resulting in them expending all their energies in a desperate attempt to get away from them.
Speaking of Pip, his surname, Pumphandle, is meaningful since when he has a penchant for handshaking and never stopping, and the way it's done, it almost looks like he's using a water pump.
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 (As an added bonus, the northeast US supermarket chain Shop Rite, which does an semiannuall canned goods sale called the "Can-Can Sale" which is advertised with an (in)famous series of animated ads featuring a parody version of the song, complete with animated can can dancers and a stereotypical Parisian artist mascot.)
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 of her as a parent.
The theme song for the "In the Garden of Mindy" skit from the Animaniacs Stew episode includes the lyrics "One's a small child / And the other's... The Brain". Seems like just a play on your expectations at first, but then you realize it neatly steps around answering the eternal debate on who is the genius and who is insane.
Segments featuring the Warners are often preceded by a sequence where they escape the tower and are chased by Ralph The Guard, and followed by one where they go back to the tower while he's still pursuing them... The odd thing about it is that he's still trying to capture them even though they're voluntarily going where he was going to send them anyway. There's two possible explanations: Either he's also supposed to make sure they're locked in properly while they're in there and can't do that when they close the door themselves, or else he's dim enough that once he gets caught up in chasing them, he forgets what the actual purpose of his pursuit is supposed to be.
When Skippy is traumatized by the death of Bumbie's mom, Slappy tries to reassure him that cartoon characters have deadly things happen to them all the time and are none the worse for wear for it, while Skippy insists that it wasn't a cartoon, it was a movie. This is kind of in line of Slappy having more Medium Awareness than him, but he's also making a distinction between animated features, which are more likely to have some serious themes, and animated shorts/tv shows, which are more likely to feature slapstick.
In the Chicken Boo sketch "The Good, The Boo And The Ugly", Lee and Eli are clearly shown to have guns, so why don't they fight back against the outlaw that's terrorizing their town? Because they're not as quick on the draw as the outlaw or the "Man with No Personality" (Chicken Boo) are, even if they were skilled with their guns.
There is exactly one Katie Ka-Boom sketch that doesn't end with the whole house being destroyed—one where Katie plans to go to prom. Her parents, fearful of her terrible temper, agree to everything she says she needs...until she starts talking about an extended curfew. Her father won't allow that, and as always, Katie changes into a hideous monster—but her father refuses to back down (for the first time ever!). They eventually reach a peaceful compromise of a slightly longer night out (Katie even says "please" while in monster form), and she transforms back into her human self. So why did this issue break the pattern? Because this time, it was Katie's safety that was in question (after-prom parties can be wild), and her father loves her too much to allow her to be harmed. He's pretty much resigned to having Katie overreact to silly issues, but if it's about preventing her from getting hurt, he can stand up to her (literally) explosive temper.
Skippy is traumatized by watching 'Bumbie' and seeing the death of Bumbie'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. Sherri Stoner says they're just on sabbatical, but even so, it makes sense that any kind of Parental Abandonment story should be tough for Skippy.
In "The Monkey Song" (not that one), Dr. Scratchnsniff invites the viewer to his house for "monkey stew." So, basically, he was going to eat the Warners. Sure, he didn't stand a chance against children that can torture Death, but geez!
Rita and Runt has a running theme of a stray cat and dog trying to find a new home or at least food. This sketch may seem innocent enough but the theme is always the same: they find a potential new home with a person that didn't have a pet and all seems well and good. However, it later turns out that their new owner didn't have pets for a reason— usually that they exploit or even kill animals for personal gain. From there on it's like the sketch is looking to find humor in pet abuse. To torture a pet is not only imitative but can be hazardous as well. Not only is it miserable for the pet, but dangerous for the child. This is likely a reason they disappeared after Season 2.
One of the sketches with Chicken Boo has him as a Confederate General who is able to Rally the South towards the end of the Civil War. He's also known as 'The Sherman of the South' and he is known to take no prisoners. Not only is Chicken Boo ruthless in war, the fact that he's a Confederate General also has serious Unfortunate Implications: It either means that a) he doesn't view certain people as people (the Slaves the Confederacy seceded for), or b) he doesn't care that certain people don't see other people as people. And considering Chicken Boo is almost always treated poorly when his Human disguise falls off...