Continuity mistake: When you are romancing a governor's daughter, and the city she lives in is captured by another nation, a new governor with his daughter is installed. This new girl looks completely different from your old romance (and her father is a completely different person), but she nonetheless remembers you. You are still at the same stage in your relationship, even if the girl has never met you before. You can even (for instance) rescue a blonde Dutch woman from her captors, and end up returning with a black-haired Spanish girl.
Continuity mistake: When you attack a city with overwhelming force, you are allowed to skip the land battle and go directly to dueling the Captain of the Guard on the ramparts. When you win this fight, by forcing the Captain into the gunpowder depot, he falls backwards through the door with his sword in his hand. Cut to an inside view of the Captain lying on the ground, and his sword is nowhere near or on him.