The portraits with the moving eyes at the beginning? It's never explained, beyond a vague implication that Manzini is fond of collecting magical items.
The reference of the Garbage Pail Kids being aliens through the implications of the trash spaceship.
The part where the Kids break out in song, since there are no other musical scenes in the movie, and this music sequence comes out of nowhere in the middle of another scene.
Bile Fascination: Given its reputation, probably the only reason most have for checking it out at all.
Darkness-Induced Audience Apathy: The absolutely vile nature of just about all the characters including the eponymous children and its dark, gritty, uninviting settings certainly lend themselves to this bigtime.
The Garbage Pail Kids prove themselves to make Juice and his gang of bullies look like saints in comparison — they steal things, vandalize property, harass others (to the point of starting fights) and even insult the two people who look after them.
Captain Manzini is intended to be the Big Good, but the most heroic thing he does is spring the Garbage Pail Kids from prison… so that he can imprison them again inside a trash can.
Fridge Horror: If they come from space, does it mean there's a whole planet of those atrocities?!? If so, it's all the reason we need to build a functional Death Star.
Jerkass Woobie: Tangerine uses Dodger and the GPK to make herself look good as a fashion designer and even ends up betraying them. At the same time though, one could feel sorry for her: it's implied that Juice is abusive as he does rough her up at times.
The Garbage Pail Kids themselves. They probably didn't intend to make them so horrific-looking, but they are.
The whole concept of the State Home For The Ugly, since it's a place where people considered "ugly" or otherwise abnormal are imprisoned and executed.
Padding: There are several long, dragging scenes of the Kids interacting. Typically scenes like this would be used for character development or exposition, but in this movie a lot of the dialogue scenes contribute very little to the film's story. Particularly of note is a three-minute sequence of the Kids playing a prank on a random man by redirecting a sewer pipe into his hot tub.
Rooting for the Empire: As… idiotic as the idea of the State Home for the Ugly is, the fact that they want to apparently outright murder the obnoxious protagonists actually makes some people want to root for them merely for that reason alone. The "kids" belong in that place, no question about it.
Snark Bait: The only reason most people who are well-informed about this movie might want to watch it.
The ship at the beginning of the film is a model that clearly looks like a "not-quite finished" model in front of a half-assed painting of Earth.
The Garbage Pail Kids themselves; already too creepy and ugly for words, it's painfully obvious that they're all just crudely made rubber suits, with poorly functioning mouths and lifeless eyes to boot.
In one scene, Tangerine picks up Dodger to go to the fashion show. As they start a conversation it is clearly daytime when they leave, and in the next shot it is now nighttime.
Tangerine and Dodger hitting on each other. She is in her twenties (or, at least, looks so) and he is almost fifteen but looks quite a bit younger. Shockingly, Tangerine's actor is only a year older than Dodger's, which somewhat sweetens the blow.
The Kids themselves who fart, piss on and threaten people every other minute despite wanting to be acknowledged and one even has a knife. They are just nasty in every sense of the word.
The Garbage Pail Kids, who engage in all sorts of unsavory acts including among others biting people's toes off, fighting, vandalism, theft, and pranking or insulting innocent bystanders.
Captain Manzini, who insists on shielding the kids from the prejudices and evils of the real world so that he can shove them all back into the garbage can where they came from, making all his efforts at the former highly hypocritical.
What Do You Mean, It's for Kids?: This film got away with a PG rating and is based on a franchise popular with boys aged 9 and up. However, amongst many, MANY other things we have underage drinking, thuggery, assault, a few curse words, near-nudity, implied genocide, sexual abuse, and murder. This actually drew the wrath of parents as well as cast member Jim Cummings and got the film withdrawn from theatres only weeks after its premiere, which resulted in the film becoming one of the bigger box office bombs of 1987 and derailing the franchise as a whole.