Demonic Spiders: The Cavalry in the old games' land battles. Whereas they can be manageable in the 2004 version, as long as you have plenty of forests to cover you, they have no real weaknesses in the earlier titles, and can easily rip your units to shreds once they get in range.
Designated Villain: The game practically encourages you to attack the Spanish. As noted on the main page, on the default settings the Spanish have the most plunder and the least ability to defend themselves from attack by pirates. Furthermore, all three plotline villains (Montalban, Raymundo, Mendoza) sail under Spanish flags, meaning that anyone going for 100% Completion is going to have to attack Spanish military ships multiple times.
Goddamned Bats: Pirate Hunters. Any Spanish ship you take out will likely trigger one or more of these ships, usually consisting of a fast Sloop. Ignore it and it will hound your fleet, pummeling it with endless cannon fire and damaging every ship you have. Engage it, and you'll likely take at least a few hits with chainshot or grapeshot before you bring the bastard down. Its never enough to actually stop you, but the damage to crew numbers and your sails is usually enough to be severely annoying.
And if you do opt to fight it, which is never a profitable venture as they are heavily armed and have few valuables in their holds, chances are the closest enemy town to you will immediately sic another hunter on your tail, and he might have an even bigger ship!
Hollywood Homely: Played straight in the 2004 version. There's really not a whole lot of difference in looks between daughters that are plain or beautiful, save maybe the size of their breasts. Subverted in the older versions as seen here; the worst daughters to marry, which were described as "shrewish creatures" really were homely.
Most Annoying Sound: BONGLE BONGLE BONGLE BONG. (This is the sound of the alarm if you get sighted while sneaking in and out of cities. Not so bad on its own, but if you play on the highest difficulty setting and try sneaking around, you will likely hear this a lot.)
Surprise Difficulty: Playing at any of the four (originally three) lowest difficulty levels isn't terribly difficult. Sure, Rogue (the second highest) is hard, but it's not impossible. But when you're no longer satisfied with a scant 30% of the plunder, you decide to bump it up to Swashbuckler for that 50% share and discover you have entered Hell itself. Storms will rip your ships apart when before they did little damage. The captains of Mail Runner ships (the smallest, least defended ship) will fight as if they were captaining a fleet of Brigs. Land combat, previously difficult, will become nigh impossible. The wind will change constantly, and always against you in naval battles. Swordfights will become a test of luck rather than skill, as apparently everyone you cross swords with trained specifically to defeat you, and Montalban becomes nigh-invincible, if notcompletely undefeatable. Suffice to say, Swashbuckler difficulty is excruciatingly hard, never lets up, and makes sure you earn whatever ending you get.
That One Level: Not a level per se, but the westernmost section of the map, in the region of Mexico, is the least popular area to be in. Getting out of it is always a long and trying process due to how the winds blow. Worse, there are only a handful of cities, and all of them are Spanish. Heaven help you if you end up here with a Spanish bounty on your head. On the other hand, depending on the version, Vera Cruz and Campeche do have quite a bit of loot for the taking.