First, let me say that I'm impressed by your efforts here! I can tell you have put a lot of time and effort into these rules. However, I have a few questions and suggestions (I apologize for the random order!):
-Gunpowder: You have a Gunpowder crit table and mention that Fire weapons cause more..uh, problems

for ships with gunpowder on board. I'm assuming there will be something in the ship's stats that tell the player if there is gunpowder on board or not? If so, it would be helpful to spell that out more clearly.
-Speaking of crit tables, I think it might be better to just condense them into one table; they don't seem all that different to me, other than a little bit of fluff text.
-Orders: It seems like some of the orders are automatic (no tests required). Is that the case? If so, I would recommend making them all either a
Ld or Skill test, as I think it would add a nice "fog of war" element. Speaking of which, what are the consequences for failing a
ld/skill test? In
BFG, failing a leadership test has rather severe consequences; no more orders for that turn! I don't know if you need to go that dramatic, but maybe no more orders for that particular ship would be in order?
-Drop the Anchor: I'm guessing that this order allows the ship to not move? The description for it seems to be missing.
-Weapons: I'm a little unclear on how to apply hits for weapons that have more than one damage type; using the Bolt Thrower example, if I were to hit the target, and then roll a 6 on a
D6, would I also cause a Crew damage? Or, if I do roll a 6, would the crew damage take affect instead of the hull damage?
-Firing Arcs: I'm assuming you are talking about each arc being a total of 90 degrees, correct? I found the 45 degree reference a little confusing.
-Turning: I think I understand what you mean, but this paragraph could use a little editing to make it clearer. As it is, it's basically a giant run-on sentence

.
-Sailing Directions: I would recommend simplifying this so that the various sail arcs are 90 degrees and line up with the firing arcs. This would also simplify the wind chart, since only three columns would be needed. (Into, Abeam, With). Either way, a simple MS Paint diagram demonstrating the various arcs would be very helpful here.
-Movement: As a sailor, I applaud your efforts to really capture the way a sailboat works with your movement rules. However, I'm concerned that the game might bog down a bit if I had to calculate the movement for a large number of ships. I can think of a couple of ways around this; you could make it so that ships are in squadrons, and movement is calculated per squadron instead of per ship. Alternatively, you could drop the mass adjustment for the Stroke Stroke Stroke order. Also, I'm not wild about the "1/2 Round Up" modifier to the Stroke number...why not just reduce the number of
D6 rolled for the order to 1 or 2 instead of 3 instead? Overall, the movement rules seem a bit too complicated to me, but it might not be a problem if there are only going to be half a dozen ships or so per side; how big of a battle were you envisioning?
-Turning: Obviously, turning will change a ship's relationship to the wind direction. However, if I understand it correctly, this does not affect the total movement distance calculated at the start of the ship's move, correct?
-Boarding/Crew: What happens to a ship when its crew is reduced to 0? Can it be captured as a prize, or is it simply destroyed?
-UGOIGO vs. Integrated Turn: I'm getting the impression you intend this game to be a UGOIGO system, but it doesn't explicitly say one way or the other. I think either would work; it just depends on your vision for the game.
All that being said, I like a number of ideas you have here. The concept of having different damage types is a really good idea, as it adds a nice level of detail without being too complicated. Also, the boarding rules seem to be a nice step up from what I'm used to with Spartan's method and also the one in
BFG; being able to assign your boarders to various areas of a ship makes it feel like I have more input into the process. Overall, I think you have a good start, you just need to flesh them out a little bit (and, of course, I recognize this is just a first draft

). I would really like to see a few full examples of some ship profiles; I'm very curious to see what your thoughts are on how the different races should be set up. Keep up the good work!
PS - Sorry for the long post, but I wanted to give your efforts the attention they deserved!