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 use 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.
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".
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, augries, fwoopers, or vampires. Havoc ensues.
Feuding Families: The McCliverts and the MacBoons (the former, possibly, transformed the latter into five legged, hairy monsters; the latter proceeded to eat them).
Footnote Fever: Not just from the author, but from Hermoine, Ron, Harry, and various others. If it's from the gang, expect it to be arguing, nitpicking, or Harry telling Hermoine 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 figurativly unlikely creature, since horses and griffins were enemies).
The Demiguise is mentioned as a huge, gorilla-like creature whose silky hair is used to create invisibility cloaks. However, even these cloaks are said to wear out over time, whereas Harry's cloak has been around for years and is still fully functional.
Also, 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.
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. No one encounters a Lethifold in-series.