Breather Level: The Delaware mission in The Warchiefs. You don't even need to go straight away to the first mission, you might even be more interested in exploring the map and getting the treasures, because you're going to need them later. Not to mention that at some point of the exploration, you'll get a Courier Des Bois (a french settler) who can get the supplies scattered across the map for you. And later you'll find a Huron native settlement where you can build a trading post so you can get even more units, which will also come in handy for destroying the ships which hold even more units. You can even get some decent artillery units before doing the first mission. By the time you're finished with the side missions, an otherwise difficult mission becomes piece of cake, and you can get a big army with just a few resources.
Crazy Awesome: Some of the cheat units are this, like George Crushington, the giant titan-bust thing that spits torches at buildings and attacks by headbutting units, complete with comic book noises and graphics, or the Monster Truck you can use to flatten entire armies and colonies in seconds.
The model of the Mediterranean Home City Cathedral is based on Florence's, despite that none of the Home Cities available are called "Florence". (Or any other Italian city for that matter)
Good luck trying to find a Catholic Cathedral resembling St. Paul's in Amsterdam.
Game-Breaker: The Sioux Rifle Rider. They have the same bonuses as melee cavalry but they can attack from a distance.
In the original game, it is the French Cuirassier. Boasting an insane 1000 HP at Imperial rank before any blacksmith and native upgrades, deals splash damage to all enemies around them that even many dedicated anti-cavalry units will still lose out to them, and like most cavalry they are fast. In large number they are almost unstoppable unless the opponent has been massing anti cavalry units.
Moral Event Horizon: In Shadow, Chayton was tracking down Crazy Horse in an attempt to negotiate peace between the Sioux and the settlers. Holme trails him and attempts to assassinate Crazy Horse, completely wrecking any chance for peace between the settlers and the Sioux, so he could take the gold from the Sioux.
Politically Correct History: The game covers the entirety of the Colonial period, but slavery is scarcely even hinted at. All of the European factions can build plantations, but white settlers work on them. The fate of the many Native cultures is also heavily sanitized. While these topics could have been covered tactfully, Ensemble Studios decided to omit them altogether to avoid any controversy.
Actually, if one looks closely enough, they will notice that some of the European settlers have dark skin. So technically, slaves are present, they just have all the rights as white settlers.
Campaign protagonist Amelia Black is another example: she is an unmarried woman who runs a powerful company and wears pants, something highly unlikely in 1817.
Scrappy Mechanic: Most players avoid naval-oriented maps altogether due to Arbitrary Headcount Limits on each ship type and the incredible strain watching a naval battle puts on most low-to-middle-end computers. A later patch fixes the performance issues with naval units, but the mortar/monitor/rocket shell explosions will still put a strain on low-end PCs.
Sequelitis: The general consensus among fans is that III fell short in comparison to the previous installments.
They Wasted a Perfectly Good Plot: Using entirely fictional stories backdropped to historical events instead of entirely historical campaigns like the previous games. Especially glaring is the ample material in North American history from the time period used in the game. This does not apply to the second expansion although it does take a few liberties with things (i.e. the Chinese being the first to discover America and erasing proof of their presence.) This is especially egregious considering that the first two Age of Empires games had several campaigns, all based on real historical events.
The first expansion had Nathaniel Black, son of John Black, as the main character of the "Fire" Campaign (which revolved around the Iroquois), and Chayton Black, the son of Amelia Black, as the main character of the "Shadow" Campaign (where you played as the Sioux). Considering the expansion pack introduces 3 new civilizations, as well as the fact that we didn't learn anything about John Black's father Phillipe in the first game, you'd think they'd have him be the main character of a campaign where you played as the Aztecs (the third civilization introduced) to complete the trifecta, but nope.
Many of the European empires present in the game actually interacted with India, China, Japan, and the rest of Asia quite a bit during the time period covered, but you wouldn't get that idea from the Asian campaigns beyond the British in India.
What Could Have Been: It was originally planned to have Sweden be one of the vanilla factions with Gustavus Adolphus as its AI leader, but they were discarded in favor of Germany. Many fans were disappointed, especially since Sweden actually had New World colonies, unlike Germany or the Ottomans. Swedish Fusiliers and horse artillery do appear in the first expansion though.
Many fans were hoping to be able to play as the Inca or Maya, but they only appear as minor factions.