I love the modeling of the rigging in this game. I have never seen anything else come as close to NA in terms of realistic rigging.
That said, there are two major types of lines that are missing from the ships: braces and sheets. Braces run from the tip of a yard (the "yardarm") to a different mast. They are used to control the rotation of the yards. Sheets run to the tip of the boom of a fore-and-aft sail, and are used to control how far out the boom can swing.
These lines seem especially relevant given that these are what the player is controlling when the player presses Q, E, Z, and C. For me, the absence of these lines is immersion breaking. Without these lines, there is nothing to control the sails' rotation and nothing keeping them in a given position.
When I've mentioned this, several people have pointed out that these lines would have to move with the sails, and so they would be harder to add. It seems like this shouldn't be an issue, given that sheets are already there in game for headsails and staysails.