Most blatantly, the fact the Miseryville is very obviously Hell. Essentially how they get away with it is simply just by not calling it Hell.
The character names taken from Biblical names adds to this even more. Lucius from Lucifer, Beezy from Beezlebub, Jez from Jezebel (though that's more Parental Bonus, as no kid would understand that — unless they had a Judeo-Christian upbringing or aren't religious, but know of Biblical characters).
This Running Gag from The Big Drip (which may count as subversion since the censors actually did pick up on it, and decide not to air the episode in the United States);
(to Beezy) You pee sitting down?
"Nobody likes a sore Heinous!"
"I'm eating carpet! I do that all the time!"
From the same episode, Beezy mentions that he has a pillow "conveniently" shaped like Heloise. Make of that what you will.
Samy's superhero outfit at the end of The Terrific Trio. Just... DAMN. "Freaky Foursome Baby!"
From The Big Date:
Samy: (to Lucius) Gee, sir, I'm flattered, but now's really not the time for pillow talk...
Speaking of Samy, you can catch him doing about two seconds of what's very obviously a strip tease in Catalogue of Misery
The season 2 episode Heads Will Roll got away with not only actually showing Heloise bleeding, but Dr. Scientist crossdressingas a disguise using eyeballs for fake breasts. And one even falls out of his shirt. And as if that wasn't enough, Dorkus crossdresses in Zombie Pickle. He even asks Jimmy not to tell Heloise.
Then there's this exchange from I Married a Weavil:
A Hair Brained Idea features... well, what do these look like to you?◊. The context doesn't help much either. Okay, they're actually just hair, but they're INSIDE OF LUCIUS'S HEAD...
In Rear Pickle, Mrs. Gerkin keeps a still-beating human heart hanging in her closet.
Mrs. Gerkin: That's just a mysterious thumping heart I keep in the closet in case company comes by!
"No one can resist a giant Jimmy!"
In "The Big Date" Heloise rips off a waitress' skin and WEARS IT AS A SUIT for a disguise.
In "A Hair-Brained Idea" an evil Jimmy rips off a monsters skin revealing muscle and organs.
A large part of the episode "Ghostsmackers" has to do with Beezy having to eat the ghost of his uneaten pizza crust. To help him, Jimmy rips apart the ghost and shoves it into Beezy's mouth while the ghost is still conscious.
In "Catalogue of Misery", in order to make a dinner out of two corn kernels, Jimmy draws a male face on one and a female face on the other, pretends to make them kiss, and then throws them into the box they came in. After the box shakes a little, tons of popcorn flies out.
This little quote from "Heloise's Big Secret":
"I've got a feeling, a Jimmy feeling, and it's not the itchy underwear!"
The episode "Spring Broke" has some pretty violent scenes in it.
For one, Beezy has his face torn off.
Also, both Jimmy and Beezy get one of their arms torn off. With some visible meat and bone.
In "The Mysterious Mr. Ten", Beezy eats a flashlight and light shines out of his eyes, nose, ears, and NIPPLES.
In "The Hooded Chicken", Beezy impersonates a panda to trick Heloise, and does a fairly racist accent while doing it.