The Black family must have tremendous military and political power. Even accounting for Gameplay and Story Segregation for building a civilization at every single level, based on the enemies they are fighting (Circle of Ossus is well armed enough to occupy Havana and the Blacks are confident enough to launch an attack on an outpost of the Ottoman Empire away from their homeland) as well as the fact they have minimal oversight and orders from higher up suggests that the Blacks are an army onto themselves. A small scale version of an N.G.O. Superpower perhaps?
Morgan Black is over 30 at the time of the Siege of Malta in 1565. John Black, his grandson, is in his 20s during the Seven Years' War (1756-1763). This looks like a pretty evident case of Writers Cannot Do Math until the end of the campaign, when it is revealed that while the Fountain of Youth was destroyed at the end of the first act, its water was still available and that Morgan (and probably Elizabeth) drank from it. Morgan is in fact still alive by the freaking 1810s, although as a very old man.
Aztec pyramids double as fortresses in III as they did back in II. At first, it looks silly, but then you realize that the Mesoamerican civilization's pyramids are not simple step pyramids, but the average person will have difficulty climbing up the stairs. Add in archers barraging you with arrows, and it becomes an impregnable defense.
John and Kanyenke's campaign is named "Ice". Several characters in "Ice", namely Kanyenke, Nonakhee and Washington, appear 20 years later in a campaign from The WarChiefs titled "Fire."
The Chinese Consulate can create alliances with the British, Russian, French and German civilizations. The end of the first Opium Wars had China signing several treaties (called Unequal Treaties) with these countries, beginning what was called as the "Century of Humilliation".
When the player gets to the Imperial Age, they get the option of building a Capitol and researching three technologies that tremendously increase the gather rates for all sources of Food, Wood and Coin. Sounds awesome doesn't it? The names of these techs are, respectively, "Large Scale Agriculture", "Deforestation" and "Excessive Taxation". These three issues became real problems during the late 19th century and the 20th century, so, in a way, the player becomes the cause of agriculture spreading like wildfire, the loss of thousands of acres in woodlands, and crushing so many people under huge debts. "It's just a tech and it's just a game!" you might say. "I'm just improving my civ's gathering rates!" While this is absolutely true, not thinking about the consequences for these actions is exactly why many politicians of the 19th were responsible for the problems caused by Large Scale Agriculture, Deforestation and Excessive Taxation.
On a similar note: fishing boats can gather food from fish or coin from sperm and humpback whales. While gathering food from fishing site eventually exhausts the food from it, a whale as coin source is infinite! That's right: throughout a game, you can station a maximum of four fishing boats around a whale (and there is usually more than a single whale on the map) and have them gather coin uninterruptedly until you move them away from the coin source or they get destroyed. Needless to say, even though at first we thought we'd never run out of them, whales turned out to be a very finite source of coin as time went by.
Carib settlements have a technology called "Ceremonial Feast" that transforms your Carib warriors in "Feast warriors" with double hitpoints. The most notable Carib "ceremonial feast" in real life was the ritual consumption of body parts taken from their enemies, which made Carib warriors especially feared. This may be the reason why Carib blowgunners are also the only Native American outlaw units in the game.
There is a tied Inca prisoner in the second Moon Lake scenario, set 250 years after the first one. We later learn that the Inca prisoners Morgan freed from the Spanish in Florida drank from the Fountain of Youth and barreled some to take home to Peru. For how long was that guy prisoner? And was he how Beaumont learned of the Incas taking the water?