An episode of season two of the television series featured some of the girls getting peeved Sybil was allowed to retake her broomstick flying test until she passed. I seem to recall Mildred was among the girls who got peeved. Milly, you got to retake it as well. Pot calling the kettle black?
Mildred didn't get to retake her flying test, she got allowed to finish it (she'd stopped halfway due to mixed fear of dark and heights). Also Sybil is a Hallow, her father pretty much owns the Academy, and her family have contributed to it for years. Mildred getting peeved can be explained by the unfair standard - she had been informed that she couldn't retake because the broom test was a way to see if a girl had magic in her, and failing it proved that they didn't. Yet here was Sybil being allowed to retake until she passed.
An episode of The New Worst Witch has Hardbroom yell that the library doesn't hve any secret passages "except that one!" What about the one Mildred had her Dangerous Old Books Society in? I can understand if she doesn't want Hettie to find out about Mildred's Society but that doesn't mean the secret passage under the floor doesn't exist.
Isn't the castle in The New Worst Witch a new castle?
Exterior shots of the castle indicated that it's the same Cackle's from the old series, although having seen some episodes recently the library appears to have shifted position. Also, from what I've heard the sets were reconstructed from the old series, but aside from that I am under the impression it is the same castle.
Why didn't Cackle's acquire enough black cats in the first place?
Because Mildred Hubble is the school's Butt Monkey, and everything she does or has sucks by default. It's probably all part of a carefully engineered plan to drive her bonkers and hopefully out of the Academy.
An in-story explanation could simply be that whoever provides the school with the kittens simply miscounted - Miss Cackle apparently believes this to be the case as she is recounting the cats and believes she's made a mistake when the numbers don't match up. It isn't until Miss Hardbroom agrees with her number that they are aware there is a problem.
How did Mildred even get into the Academy, considering her complete ineptitude? Surely there must be an entrance exam of some kind. Or are we expected to believe all witches are accepted, regardless of ability?
In the tv series Miss Cackle explains to Mildred she enjoyed her story about the two-headed giant who argued with himself all day, showing that she had a great imagination and so Cackle took her in thinking she had potential. Of course that only explains the tv series, and not the original books, so I got nothing.
Another suggestion used in the TV series that may be considered is that all magical schools are required to take in so many scholarship students per year. Mildred may have simply been there to meet a quota.
There is also the statement by Miss Cackle in the first episode that the right words in spells aren't as important as the right feelings. Therefore a student with a good imagination is likely going to have a better time casting spells than someone who's too by-the-book.
Is it just me or is Tim Curry trying extremely hard to be David Bowie during this movie?
Miss Gimlett. She's only mentioned in the season 2 premiere so what did she teach before she left? It's made pretty clear in the show that Miss Cackle taught spells, Miss Bat chanting, Miss Hardbroom potions and Miss Drill PE so what did Miss Gimlett do beside act as the Year Head for the 2nd years?
Mildred getting in trouble when Enid cast the spell on her in "Miss Cackle's Birthday Surprise". Mildred materialised in front of Miss Cackle and Miss Hardbroom and then she disappeared. They saw she didn't say any spells in front of them and still disappeared so obviously someone else had to be casting it. Yet Mildred is the one who gets in trouble when she clearly wasn't casting a spell.