Bull Sharkowski is the school bully in the series. In real life, bull sharks have rather high levels of testosterone in their bodies making them more aggressive than most sharks (making them the most dangerous sharks in the world, yes, even more so than the more (in)famous great white).
One episode involved Adam and Jake going to a human school for a day. When Jake sees the other human classmates, he sees in his eyes that all of them look exactly like Adam. Why? We as humans mostly see animals of the same species as exactly the same, so thus a monkey could not distinguish other humans by physical appearance.
The idea of a human in an all-animal school actually makes some sense. Humans technically are animals, just more evolved than other animals. So, technically, Adam is an animal. (Granted, not a lion, as the whole typo incident led everyone In-Universe believe, but still...)
As mentioned on the main page, pixie frogs are actually bigger than most frogs, but there are still jokes about Principal Pixiefrog being small. However, the jokes still make some sense when you consider the following:
While pixie frogs are bigger than most other frogs, most of the animals that attend/work at the school are bigger than frogs in general.
Pixiefrog could be small by pixie frog standards, thus meaning he's not just tiny to the animal public, but to his own kind.
The Spiffies are the smartest kids at the school. The five members of the group are a dolphin, a pig, an elephant, a squid, and a parrot. All five of those animals in real life are generally considered to be some of the most intelligent non-human creatures on Earth.
While is the resident crocodile character presented as a nerd? Because crocodiles are intelligent even by reptile standards, being able to learn faster than rats (which are also known to be brainy).
In "I Got a New Aptitude", Jake and Adam were depressed, when they learned they'd never achieve their dreams in the future, and instead become zoo animals. Cut to a sad montage, along with a sad musical number. The scene itself seemed innocent enough, until you realize the first lyric of the song was "What's the point of going on, when you're future's been decided?" The first half of that is usually a quote said by people having suicidal thoughts, often saying "What's the point of going in living?" Were Adam and Jake contemplating suicide, feeling their lives were predetermined to be miserable and unsatisfying?
If you look closely at Windsor's plate, during a cafeteria scene in "Shark Attack", you'll notice he has what looks like a chicken wing for lunch. Why would a school for all animals, including that of the poultry family serve that? This is similar to the Pokémon predicament, where human characters eat meat in a universe, where the only other living species that it could come from are the well-beloved Pokémon creatures.
In one episode, the entire school ceiling is covered in what appears to be asbestos...which Jake consumes under his assumption that it's popcorn. It later turns out to be a large mess of bat guano, so Jake is safe, but had it been asbestos, just how many people in the school would know about it if Jake wasn't eating it?
A not-so-subtle fridge horror joke would be in "Where in the World Are Adam's Parents?" The concept of the episode is already extraordinarily dark for a kid's show, with Adam's friends and teachers assuming he'd eaten his parents. At the end of the episode, it was learned that Adam never did this, as he brought his parents to school, wearing hazmat suits that covered their bodies and muffled their voices. The cast shared an Everybody Laughs Ending, but at the very last second, Adam burped, and a bone came flying out of his mouth. He and everyone else looked at it in shock. This was not explored anymore, since the episode ended right there. So, it was basically proven that Adam was in fact a cannibalistic murderer, simply as a one off joke, so even if he didn't kill his parents, he's at least killed someone and eaten their bodies.
In fact, since his "parents" were completely obscured by their costumes, it makes you wonder, if he really did kill them and just paid two random stand-ins to wear that instead.
When you think about the concept of the show as a whole, and take the whole "animals" element out of it, the show's premise becomes really dull and depressing. A 12-year old boy named Adam Lyon, is abruptly transferred to a new school in the middle of sixth grade. There, he feels very unsafe and left out, being bullied by bigger kids, and flunking academically, with every new subject, alienating him beyond reasoning. He experiences constant melancholy over the loss of his old school. In the end, his future gets derailed far off from what he originally wanted, having been forced into a new field, which he'd be working the rest of his life, when he was simply a mere 12 years old. Kind of makes you think how depressing the show would be, would it be altered to be as realistic as possible.