Alternate Character Interpretation: The Big Bad Wolf. While people know him to be a predator who tricks a little girl into telling him about her grandmother, other versions have a more disturbing take on him. The song, "Little Red Riding Hood", has him be a Stalker with a Crush who just wants to walk with Red through the woods. Other darker versions have him be a sexual predator who tries to take Red by force. Yikes.
Big Lipped Alligator Moment: In some versions where the wolf tricks the girl into eating some of Grandma's dead body and blood, a cat suddenly comes to call her a slut because she eats her grandma... then the cat is never heard again. Clearly Grandma lives in a very strange neighborhood.
Critical Research Failure: One of the primary instances to invoke this with fairy tales. Lots of people are unaware of the history.
Such as Perrault so far being the first known to ever used "red" importantly in the story.
Bringing up sex symbolism even though the versions where sex was in the story predate both Perrault and Brothers Grimm and were not included in their versions.
Werewolf inclusion, a lot of people think this is a modern addition even though older versions did indeed call the wolf a "loup garou".
Freud Was Right: A common interpretation of the tale is as an Aesop about a young girl's burgeoning sexuality, with the wolf standing in as a sexually aggressive man. The red hood is often interpreted as representing menstruation, carnality, virginity, or sin in general.
The musical Into the Woods may be going with this interpretation, mainly the original '80s stage version where the Wolf has, ahem, visible genitals.
Moral Event Horizon: The wolf crosses it in the versions where he feeds Red her dead grandmas remains.
Nightmare Fuel: Perrault kills off Grandma, then has Little Red tricked into becoming a cannibal, and then she too meets a gruesome end in the wolf's jaws. Sleep tight kids.
It's also often a point people think the Hotter and Sexier versions of the story are a new idea. Even though versions where the girl is older and hints of sex or direct sex used to be a regular part of the story.