An Aesop: Although couples falling out of love is possible, just because one's parents fight once doesn't automatically mean they don't love each other. Even loved ones may fight on occasion.
Bullying the Dragon: At the end of the episode, Dongwa taunts the Sleeve Dogs, despite that they have him outnumbered three-to-one.
Heel Realization: When Mama Miao angrily points out how his singing has woken up everyone in the palace, Baba Miao is clearly ashamed at what he's done. He realizes it was inconsiderate of him to do it at night of all times when everyone else was trying to sleep.
Hell Is That Noise: Baba Miao isn't the best singer there is. Mama Miao even tells it to his face. The only thing worse than when Baba Miao sings is when he sings with his own alley cat friends.
Innocently Insensitive: Oblivious to how Chinese checkers means just as much to her as singing does to him, Baba Miao was a bit inconsiderate to say "what [Mama Miao] does is just a game".
Parents as People: Explored. Mama Miao and Baba Miao do argue a bit in this episode (and accidentally do so when their children listen in on them that night), but by no means do they want to do so with their children present.
What the Hell, Hero?: Mama Miao calls out Baba Miao on how his nighttime singing has not only woken everybody up (their own children included) but chased away Nai-Nai from their game.
Cats of a Different Class
Actually Pretty Funny: When Sagwa first experienced how uncomfortable the booties were, the Bei-Xing cats were pretty amused at her pained reaction to their tightness. Later, when the Head Cat reminds Sagwa of how uncomfortable the booties were, Sagwa can laugh at the experience looking back.
An Aesop: Sometimes, the simple things are the best in life. Just because something seems beautiful or fancy doesn't necessarily mean it's comfortable or even enjoyable.
Artistic License – Animal Care: The Bei-Xing cats are fed rice because if they ate fish, their breaths would offend their master. The thing is, cats are strict carnivores and can't afford to eat rice, much less on a daily basis. Justified, as it's a time before proper animal care was invented, and on top of that, the Emperor's Cousin doesn't care about his cats anymore than he sees them as accessories.
Be Careful What You Wish For: Sagwa wanted to try on the Bei-Xing Cats' slippers for herself, but to their amusement, the novelty quickly wears off for her, as they feel uncomfortably tight on her feet.
The same could be said for the Bei-Xing cats, who often wish they could have at least one moment without their booties. After they play in the mud to celebrate that moment, they realize their muddied paws could easily give away to their master they took off their booties, and he'll no doubt make good on his threat to make them strays.
Because You Were Nice to Me: Sagwa gives the Bei-Xing cats fresh shrimp (the first decent food they've had in a while) in exchange for giving her their booties to wear. Since the slippers are uncomfortable to begin with, the Bei-Xing cats get the better bargain as they get to eat good food and spend a short while free from their hated slippers. What's more, Sagwa is kind enough to (with her family's help) wash their muddy paws so they won't get into trouble. In return, before Mama Miao can scold her daughter for allegedly getting them in trouble, the Head Bei-Xing Cat speaks up for Sagwa and informs her she did them a good turn.
Comically Missing the Point: When Baba Miao explains that the Magistrate's guest (the Emperor's Cousin) has traveled across rivers and over mountains, Sheegwa voices how that's a long way to swim and climb. Dongwa has to set the record straight that he didn't travel all that distance himself.
Did Not Think This Through: The Bei-Xing Cats get their wish of spending a short while without their booties, and promptly play in the mud to celebrate their newfound freedom. But not long after, it occurs that with their paws dirty, their master will suspect they took off their booties and banish them to the streets.
Surprisingly Realistic Outcome: Sagwa keeps thinking that the Bei-Xing cats' beautiful slippers will be just heavenly to wear. But when she tries them on, she learns the hard way that they actually feel tight and uncomfortable. After all, cats aren't made to wear booties.
Wham Line: From Sagwa's point of view, she's very surprised when the Head Bei-Xing Cat off-handedly mentions he and his fellow cats are "not happy". It baffles her why such imperial cats are unhappy with living such luxurious lifestyles.
