These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Brilliance: Ethel gives herself a "witch-over" in season 2 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 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.
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.
Les Yay: In The New Worst Witch, Dyllis Mustardseed seems to be crushing pretty hard on Belladonna Bindweed. Too bad Belladonna hates her.
Older Than They Think: An isolated medieval castle containing a magic school, with a forest nearby? A protagonist who has no prior knowledge of the magical world? A rival who comes from a leading magical family? A hook-nosed Potions teacher who favours the rival and despises the protagonist? A kindly, grey-haired Head who befriends and helps the protagonist? Classes in Charms and broomstick riding? While both The Worst Witch and Harry Potter clearly have very similar elements, Jill Murphy's series predates the latter by 23 years, with the first book being published in 1974.
Painful Rhyme: Tim Curry's big song features every conceivable word that rhymes with "Halloween," and many that aren't.