Nightmare Fuel: In some cases. Especially when accident-prone 'rabbits' come into the picture. Also the invisible castle and how to get one *shudder*.
Real Women Don't Wear Dresses: In-universe, the princesses who aren't like Cimorene (meaning most) are often seen as stupid and useless for embracing their Damsel in Distress heritage and being happy with being rescued and married. Cimorene herself, however, admits they are silly but can't really help it, considering that's just how they were brought up.
The trope is played with in that while Cimorene goes on adventures and uses a sword, she also is fine with doing traditionally feminine things like cooking, cleaning, and dressing up (see: her absolute pleasure at discovering her wardrobe at Kazul's is magical and can provide practical work dresses and luxurious gowns as needed). The first book also subverts this with Alianora, who tries to be a proper princess but fails miserably in various ways (and it's mostly not her fault - aside from the spinning straw into linen thread thing). She still is Cimorene's best friend.
Also, see Morwen, who wears robes (close enough to dresses), makes cider, bakes gingerbread, and gardens deadly nightshade, apples, and lilies. She's also a very powerful practical witch and magic user.
Squick: The wizard disposal method, amongst other things.
What an Idiot!: It becomes clear rather quickly that Anteroll isn't very bright. In Dealing With Dragons, he accidentally lets it slip that a security spell his father proposed for Kazul's lair was very easy to do (judging by Zemenar's reaction, Cimorene guessed that he was planning to pretend it was difficult, as an excuse to snoop around). In Searching For Dragons, he comes to visit Cimorene in, what she points out, is a very suspicious manner (he comes blundering in the back way without announcing himself or bringing a candle). In Calling On Dragons, he is captured by one of Morwen's cats (he was shrunk at the time granted, but still), and is referred to by Telemain as "the wizard Cimorene keeps melting". The epilogue has Cimorene tell how he was so determined to get revenge on her that when he found her hiding place, he walked right past Mendabar's magic sword and Cimorene's child and tripped over Kazul's tail before he was melted. In Talking To Dragons, he completely loses any intelligence he has, being melted by Cimorene in the first chapter just after boasting that he will kill her and take the sword and Daystar. From there, he continues to ineffectually stalk Daystar until he is finally gotten rid of when he decides to sic a monster on Cimorene...right after her son just learned how to effectively wield the sword that channeled all magic in the forest.
Arona Vamist from Calling on Dragons counts in a big way. He basically decides for no reason to act as a weird variation of a Moral Guardian, trying to force people to conform to the "traditional" ways for things - forcing witches to have one black cat, driving an angry group of Fire Witches out of town, etc. It's later revealed that he did have some protection from the wizards, but that doesn't explain why, when he lost said protection, he thought it was a good idea to contradict Kazul of all people on the behavior of dragons. He also tried to take the moral high ground against the protagonists "kidnapping" him, even though he was an accomplice to the wizards stealing Mendanbar's sword, which also meant he was an accomplice to their plan of invading the Enchanted Forest.