I would to see some more detailed damage models and repair details, similar to Napoleon: Total War. When you repaired your ship, you could see make shift wooden boards covering up any cannon ball holes. Also not sure if it's in the game, but cannons should be destroyable, and you should see them off their carriages.
I think the ships should be a bit more alive (definitely help with emersion and getting attached to the ship), as someone said you should have an avatar on the poop deck, barking out orders. I think you should see slightly better dressed sailors-signifying higher ranks walking around the ship. Sailors up the rigging etc. Bigger ships could even have a complement of marines onboard shooting at close enemy ships. And More smoke! Smoke in extended close quarters engagements was definitely a big thing! I know the game has smoke now, but it would definitely help with realism if huge smoke clouds were floating around after two massive broadsides.
Could you also maybe add fire by deck to the multiple decked ships, might be handy in rough seas to be able to shoot without wasting a decks worth of shot over the enemies ship.