These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Crowning Moment of Funny: A lot of care went into giving each building's ambient sounds, as well as their walkers, a distinct humorous flavor, even if many of them are stereotypes.
Acrobat School: "Whoa!" *crash, sigh* "Okay, forget the plates, can you juggle?" Copper Miner: "Here's your copper, you slave-driving boss man!" Acupuncturist Hut: "Don't worry, I'm very skilled." *pained moans* "Sorry." Tax Collector: "You all know it's better to give than to receive, especially to me — er, I mean, to your government."
The Fishing Quay worker animation has one of them hitting the other with a fish as he defends himself with his hat, then when the catch comes in the former throws the fish into a crate over the head of his co-worker who ducks to avoid them. And at the Daoist Temple, the two monks bow in unison, only to bump their heads.
Game Breaker: Many Heroes come with benefits that snap the difficulty of a mission in two.
Sun Tzu fittingly makes military action a breeze. He halves the construction costs of forts and fortifications, makes it cheaper to hire spies, captures any disguised enemy spy he finds patrolling the city, reduces the travel time of armies, improves infantry morale, and when in combat himself he's one of the best offensive heroes. If you plan to attack an enemy, Sun Tzu can make or break the attempt.
Guan Di can bless a fort with free loads of weapons or warehouses with free loads of bean curd, while Xi Wang Mu can bless a jade carver's studio with a stock of raw jade. Build a row of warehouses/forts/carver studios and send them down the road handing out blesses for tons of free goods.
Good Bad Bugs: The game handles attacking rivals oddly if you conquered them while their army was on the way. Bribing the rival army suddenly makes the vassal a normal trade party, and fighting them off keeps things normal and surrendering makes you their vassal as expected. When it comes to a city that has conquered you attacking to quell your rebellion, if you fight them off it's possible their city will become your vassal as a result.
Designated Hero: As any history major can tell you, many of the the rulers you're working for aren't looked back upon too fondly by today's historians. Also, as far as the mission briefings are concerned, anyone who isn't a part of China and doesn't serve the Emperor loyally is a barbarian and should not be trust.
Scrappy Mechanic: Religious worship, particularly the heroes. You have to pay tribute to them to increase their level of happiness and getting them to a level where they're likely to visit your city will require several months tribute of high-priced goods, and continued tributes during their stay to keep their happiness up and keep them around. The Ancestor heroes are the worst though — the other three pantheons have their heroes always at Contented, but Ancestors will fall to Neglected, Unhappy and eventually Angry, and when they get Angry, they may decide to unleash a natural disaster on you as punishment for not paying them lip service. And finally, unless you have the objective to have a hero visit for so long, the only reason you'd want a hero in your city is to use their services, usually blessings — except each blessing lowers their happiness rating again.
That One Level: A lot of the levels set in the desert. They usually have one large grassy area, limiting where you can build your city (Wells are needed to get beyond the most basic housing levels and can only be built on fertile ground), forcing you to build several more farms than usual due to the infertile ground limiting their growth, your only reliable source of income is probably going to be salt and whatever metal of the age your smelters produce, and occasionally ceramics. Furthermore the earlier missions which use Wood for tax collection require you to import it since trees of course are of short supply in a desert. A Han mission even has you building the Great Wall, which requires hundreds of units of Wood, thus meaning you're going to spend the entire mission importing it and have to come up with exports fast so you can afford to.