Crack Pairing: Some people seem to ship Nanny Plum and Wise Old Elf for no reason other than that they fight a lot in the show. Some people, especially parents of children who watch the show, like to call this a case of Belligerent Sexual Tension.
Demographically Inappropriate Humour: In "Daisy and Poppy's Playgroup", there's a gag where Queen Thistle's panties (even explicitly being mentioned as such, at least twice) get left behind when she gets teleported to the land of the dinosaurs.
The Wise Old Elf is widely hated by fans, mainly for bullying the fairies for their lack of common sense, especially since some of the fairies do have common sense (like Holly or Queen Thistle). He is also hated for being called wise when he is really The Ditz.
King Thistle definitely gets the most hate — like the Wise Old Elf, he often gets called wise when he is really The Ditz, and is shown to be very rude, lazy and spoiled. He never seems to care about anyone else but himself.
Queen Thistle definitely, she has a husband that is very lazy, whom she really is clearly more intelligent than, plus her sister Queen Marigold is shown to bully her, to the point of Queen Thistle freaking out whenever she has to see her.
Holly is also shown to get this trope a lot. Specifically, in the episodes "Elf School", "Visiting the Marigolds" and "The Wand Factory" it is clearly shown that Holly wants to live a normal life (even implying that she wants to be an elf or even a big person) instead of living the annoying fairy life.