An Aesop: Rules aren't simply there to spoil your fun. They're meant to keep you safe. Sometimes, rules don't necessarily have to be broken in order to have any fun.
Everybody Has Standards: The Magistrate may be relatively strict with his rules, especially when he catches the Miao siblings tracking puddles into the palace. But when he learns Sheegwa has caught a cold, he softens significantly.
Explain, Explain... Oh, Crap!: Sagwa and Dongwa have this thought process. They imagine how fun life would be without rules. They could do whatever they wanted, when they wanted. But when they try to imagine all the mischief they could put Reader up to, it dawns on them: without new rules to announce, the Reader would be out of a job. And likewise, their parents would be thrown out of the palace, since there would be no use for cats who write the rules.
Ironic Echo: Whilst complaining about rules, Sagwa mockingly recites the rule about not climbing the wall because they'll "fall and be swept away by the sea". Later, when scolding Sheegwa for climbing the wall, she finds herself remembering her earlier words and saying them rather soberly.
Pet the Dog: The Magistrate could've punished the Miao kittens as soon as he learned they not only tracked puddles into the palace, but also broke the rule about walking on the wall. But he doesn't. Instead, he has the kittens given a bowl of broth to restore their health. What's more, he invents a rule that anyone who falls into the ocean (by accident) shall be given a bowl of broth.
Surprisingly Realistic Outcome: Discussed. Sagwa and Dongwa think to themselves how much fun it would be to do whatever they want in the palace, whenever they wanted. But then they realize that without rules, the Reader be out of a job, since there would be no rules to decree. What's more, their parents would be rendered jobless as well if they had no new rules to write.
Ciao, Miao
Earn Your Happy Ending: After worrying for a while that one of them would be taken away to Italy forever, the Miao family can rest easy knowing they'll stay together.
Nice Job Breaking It, Hero: Sagwa and Dongwa had the idea of coating themselves in ground pepper so Marco Polo's descendent would think he was allergic to them. By neglecting to coat Sheegwa in pepper as well, it ends up convincing him to decide he should pick her since she doesn't make him sneeze.
Papa Wolf: When the time comes for Marco Polo's descendent to pick which kitten to take home with him, Baba Miao starts hissing, as though prepared to defy any of his children being taken away forever.
Refuge in Audacity: In exchange for the cats, Tai-Tai offers up a (badly done) painting of the Magistrate's ancestor and Marco Polo's first meeting. As it turns out, Marco Polo's descendent loves it!
