Dark Is Evil: Any beast or being classified as a "Dark Creature" falls under this. Dark Creatures (or "Demons" as they are classified) consists of anything that is capable of magic and uses said magic for the sake of malicious intent rather than survival. Dementors, werewolves, and boggarts are all considered Dark Creatures whereas chimeras, manticores, and dragons are not. This is because a dragon will only attack a wizard (or Muggle) to defend itself or for food while a werewolf will attack to turn another human into a werewolf or out of murderous intent.
Deadpan Snarker: Have you read Harry and Ron's commentary? There's also the arguments Ron and Hermione get into.
Early-Bird Cameo: Many creatures first appeared here before being mentioned in the books. Even Thestrals are included, albeit as a minor reference under "Winged Horse".
Then there's the erumpent, a rhinoceros-like creature that has an exploding horn. In Deathly Hallows Xenophilius Lovegood has one's horn on his wall (thinking it belongs to a Crumple-Horned Snorkack) and his accidentally blowing it up helps the trio escape.
Exact Words: Early definitions of "Beings" were done with human centrism in mind, leading to definitions like "creatures who walk on two legs" or "who speak the human language." This would leave out obvious beings like centaurs and merfolk, but accidentally include a lot of creatures, such as trolls, augureys, fwoopers, or vampires. Havoc ensues. The definition that stuck was "Any creature that can understand the laws of the Wizarding World", which helped tighten the list to just sentients.
Feuding Families: The McCliverts and the MacBoons (the former, possibly, transformed the latter into five-legged, hairy monsters; the latter proceeded to eat them).
Foreshadowing: The Demiguise is mentioned as a huge, gorilla-like creature whose silky hair is used to create invisibility cloaks. These cloaks are said to wear out over time. Harry's cloak has been around for years and is still fully functional, becoming an important plot point in Harry Potter and the Deathly Hallows.
Footnote Fever: Not just from the author, but from Hermione, Ron, Harry, and various others. If it's from the gang, expect it to be arguing, nitpicking, or Harry telling Hermione and Ron to stop arguing.
Not the Nessie: There is one, but it's part of a larger species, and is a shapeshifter - it turns into something else whenever muggles look around for it.
Our Dragons Are Different: The book obviously depicts every single species of dragons in the Potterverse. Most seem for some reason to be European (even the South American and Australasian species), with only one species based on Chinese dragons, and even so being more akin to European forms as it breathes fire and is malevolent (although all of them are more animalistic than anything, harkening back to the pre-Tolkien versions of the myths).
Our Griffins Are Different: Classical griffins and hippogriffs (note that hippogriffs were a part of mythology, but mostly as a figuratively unlikely creature, since horses and griffins were enemies).
The Nundu is described as the most dangerous beast in the world. You would guess that Harry has to fight one later in the series. He doesn't. Then again, it lives in Africa, where Harry really didn't have any reason to go...
Ditto with the Lethifold, which requires a Patronus Charm to repel. Around the time this book came out, we'd only seen Patronuses used on Dementors. Yet no one encounters a Lethifold in-series.
All of these are probably due specifically to the remote location of the beast, Nundus being East African and Lethifolds being tropical, though.