In the first episode of the 1998 series, why does Ruby obviously start directing Mildred so closely to Ethel (leading to Ethel ratting them out)? Because it's only the first week of school and they wouldn't have had time to know how much of a brown-noser she is yet.
The most obvious example would be seen in the portrayal of Miss Hardbroom in the adaptations. While Mildred sees her as a teacher who hates her, the audience are shown that this is not the case, it's simply that Miss Hardbroom thinks that the girl keeps jumping into trouble without thinking about the consequence (this is outright confirmed in the first episode of Weirdsister College.) But of course that wouldn't be obvious in the books - they're all from Mildred's point of view.
Ethel gives herself a "witch-over" in season 2 of the 1998 series because she's embarrassed by her sister (explaining why she is played by Katy Allen). However in Weirdsister College she is played by Felicity Jones again. Now she's at college where her sister isn't there, she doesn't have to worry about being embarrassed by her so she removed the "witch-over". Likewise Deirdre Swoop doesn't recognise Ethel in the first episode because she had only seen her witch-over self.
It's stated in the first episode of the 1998 series that the right words in spells aren't as important as the right feelings. Episode three deals with Ethel being turned from a pig into a duck by Charlie getting the spell words wrong. The brilliance is that Charlie has not been educated in magic at all so he can't rely on "the right feeling" - so all he can go on are the words to the spell. Alternately he might have been concentrating on "turn Ethel back from a pig" but not concentrating enough on what to turn her into.
Closely related is Enid's spell for food in "Let Them Eat Cake". Like Charlie, the spell fails because of the last word. Both she and Charlie put emphasis on the last word in the incantation - resulting in the wrong effects. Charlie says Reduccio as "re-DUCK-io" so Ethel is turned into a duck. And Enid says "make it hasty" and gets them showered with hay. Also for Enid's spell - hay can be a snack for animals. Enid just wasn't being specific enough that she wanted food for herself.
In the 1998 series, why are spells in Latin when any incantation will do (coupled with the right feeling)? Because Cackles prides itself on tradition and Latin was what the upper classes wrote books in back in the days the spells were invented.
In the season 1 finale of the 1998 series, why doesn't Agatha (disguising herself as Miss Cackle) notice the students and teachers whenever they spy on her in "A Bolt From The Blue"? Because Agatha can't see properly through Amelia's glasses.
In one episode from season 1 of the 2017 series, Mildred is teleported into the potions lab after being late for her lesson. At the time, Mildred was clutching onto a spire on the roof of the castle. This scenario present a couple of Fridge Horror situations:
It is a good thing she was not teleported while she was sitting on the toilet.
It is a good thing that she was teleported off the roof, as there was a chance she could have fallen to her death.
In an episode from season 3 of the 2017 series, Ethel casts a spell to drop paint all over Ms Hubble. If the paint had gotten in her eyes, as it nearly did, she could have suffered severe and permanent vision damage.
Though it's Played for Laughs, as in Harry Potter, the fact is that memory-loss potions, love potions, and plenty of other potentially incredibly dangerous potions and spells are readily available and easy to make—they could be used for much nastier things if this weren't aimed at a younger audience.
Such things are against the Witches' Code however, which is taught from the very first day the girls have. So they're explicitly illegal and punishable - and the girls are also taught reversal spells and potions. And really, the witches do use spells for nastier things; Agatha and her army were going to use an invisibility potion to sneak into the school and turn everyone into frogs. And in the 1998 series, Miss Cackle was turned back with a reversal spell easily. It would only take one person to be able to carefully avoid the witches and reverse their spells.
Then there's the Dr Foster Effect, which means that any magic done for particularly selfish purposes will backfire on the caster if they're not careful. Agatha and her henchwomen looked like they had to go to a lot of work to sidestep that, which still left them open to being caught by Mildred.
