I'd like to see musket men on the masts, waisters walking around on the decks, some men in the masts made to look like they are modifying the rigging, a helmsman, and perhaps a few officers and midship men located in various places to create some sense of order.
I'd also love an additional camera that is restricted to the decks and stairs of a ship, making it seem more of a first person experience, but its understandable if this isn't implemented.
A "fire as she bares" mode would be great to allow your gunners to fire as she sees fit, historically accurate while you steer your ship.
For the upgrades that involve humans, like powder monkeys, boatswains, marines, I'd love to see buying them at the lowest level and training them up to mastercraft through battles like the officers. At the moment, the only way to get them is have already found them in the early days of the wreaks being introduced.
A far better boarding system needs to be introduced. Perhaps you can force the boats when boarding to the same direction, and creating animations for the people fighting, with smoke puffs from the tops for the muskets, smoke clouds from cannons, shrapnel from grenades on the oppositions deck, and for the attack (excluding the boarding from ship to ship part) perhaps a cutlass fight on the main deck.
I am very happy with the increased weight carried by fighting ships, and I would very much like it if the enemy ai had the ability to surrender. A trades cutter, lynx, and brig have nearly no defense against a rattlesnake, and after a certain amount of damage to the chase, such as say 50% of the sales, gradually increasing hull damage depending on the ship (a cutter and lynx requiring only a little damage to frighten the crew to surrendering where as a snow would not give up so easily) surrendering is a completely logical action. Since a chase takes 10-15 minutes on average to gain only a very small amount of resources and a ship to take apart (usually only giving 5-10 parts), shortening this time wouldn't be asking for too much.
For the sake of realism, when sending ships to an outpost after capturing them, sending a small amount of crew along with them would be realistic as well, a prize crew that is. the larger the ship, the more men.
There are a couple of activities I would like to see. Whaling would be a great addition and was common for the time. Rare fleets of traders would be great as well that you would need a fleet of three ships to take them all. And perhaps more controversial, slave ships to take and free. This was done by the British in the blockades of Africa, and it would not be out of possibility to do in the Americas. One of the most desired things to do however, is hunting a ship around the world. Say going from port to port to know where the ship has gone and slowly but surely track her and bring her to action. This could be a special event to award prizes, and would be hard enough or long enough that every one could complete it if given enough effort instead of the current wreaks of fleets awarding the lucky one person to get there first.
The ability to order your ships in fleet to board would also be nice. Since you own the ships and since you crew them with your own money, I would like to see the ability to upgrade them in the ways you see fit. Hiring additional officers for them would also be nice.
For the crew of ships, I would like to see the cannon loading, the sail setting, and accuracy all dependent on the rating of your crew. Landsmen vs able, men of war vs lubbers based on the experience they have in battle. since most naval actions did not fight to the last man (like a cutters crew will ) being out numbered would lower the morality quickly after each turn. How can a crew of 60 possibly fight a crew of 200 without losing faith so quickly?
Perhaps in battle, depending on your marines, you could shoot at the enemy's men when in a certian range. This would make the battles faster. Perhaps even making muskets a separate set of guns to be fired like you fire the cannons! Perhaps even set to ai mode like the suggestion for the cannons above.
I have so many other suggestions, but I think this is quite a large enough bite to chew!