The following are things I consider to be "minor" tips. Following them will not necessarily make you an awesome puzzler. But if you're stick at distinguished for some puzzle, the following should help you jump that fence.
First some general points:
Speed vs Efficiency: With the exception of bnav (which I won't cover), all of the piracy puzzles are either "speed"or "efficiency" puzzles. With efficiency puzzles, each move you make loses you some score. With speed puzzles, how many moves you make are irrelevant; what matters is how quickly you perform the puzzle. This is important when working out the best strategy to use. I will list which of these a puzzle is below.
10 second move: For all puzzles, you lose score for 10 seconds of inactivity. This is so you don't laze on station and maintain an incred for something like rigging. Note, also, that when the game is paused counts towards this time. Not totally sure what counts as a "move" in sailing and navigation - if its actually per drop or per you just moving the piece about.
Specific Puzzle tips:
Bilge - Efficiency puzzle
The main thing to remember is that Combos (e.g. 3x3, 4x5 bingo, sea donkey) are where the points are. Long clears and cascades (i.e. when you make a clear, and then another one pops up as a result of that click) are worth relatively few points; don't focus on them.
Try to make 3x3s with 1 or 2 clicks, bingos (e.g. a 3x3x3) with 4-6, seadonkeys (3x3x3x3)... well don't worry about them unless you see one. It is usually worth it to spend an extra click to extend the length to 4 or 5 - so 3 clicks for a 3x4 - but no more than 1 click. If you can't do a move in so few clicks, make the combo which is closest to the number of clicks to expend (and 1 extra click for a bingo is better than 1 extra for a 3x3)
If you can't see any of these, make the largest single (e.g. a 5) you can see with 1 click.
Clear from the bottom if there's lots of stuff you can do, so you don't disturb things. Clear from the top if you want to break stuff up cause there's nothing much to do.
Finally, note that clearing crabs gives you score. Importantly, the higher the water is, the more score you get. It is possible to get incred by just clearing crabs when the water is high, so if the water is very high just focus on clearing crabs.
Treasure Haul - Speed Puzzle
Thaul bears a cosmetic similarity to bilge, but with the rotation sideways. DO NOT THINK OF IT LIKE BILGE.
The scoring couldn't be more different. Scoring is almost entirely about how many pieces you clear - it doesn't matter how. Gems, cascades, combos... whatever. Just clear as fast as you can. Combos are better only in that they clear more at once, so just clear whatever you can see as quickly as you can.
Also, clear from the top; at the top you are more likely to disturb the lower ones causing cascades for an added bonus.
Speed is the key. You should be constantly clicking.
Carp -Speed Puzzle
Speed is paramount in carp. You actually gain score for placing pieces (note: not if you place a piece incorrectly so its not entirely fitting in a whole).
Start from the outside and work in. Try to avoid making spaces that can only fit one type of piece. Use your bad pieces early on in a place where the are relatively ok. Alternatively, use bad pieces to fill holes you've already booched up.
Work on each of the holes at the same time, don't just focus on one. Also, DO NOT finish two hole which are diagonal to eachother - you won't get new holes and you will struggle to MP the remaining two because you will lack choices.
Finally, when you are 2-3 piece away from completing a hole, do NOT immediately place a piece in it as soon as you get the one you need. Work out what you might need to fill it, then hold the piece in your toolbox until the last possible moment (or until you have all the pieces you need to complete the hole) to maximise your chance of getting the rest of them. The same goes for putty; keep it in the toolbox until you HAVE to use it to save a masterpiece.
Rigs - Efficiency Puzzle
Pulls of < 5 pieces are NEVER worth using a move to get. Longer pulls are worth MUCH more than shorter ones. Consequently, it IS worth it to spend a move to extend a pull from, say, 9 to 10.
Moves that get you bonus pieces also give you a large score bonus. Try to include one of these into as many pulls as you can.
It is absolutely worth taking the time to make a larger pull. Try to make a good sized one every 3 moves or so, but never plan to do something that will take you more than 6 moves.
Sails - Efficiency Puzzle
So cascading (clearing and then the pieces drop down to make another clear) is where the points are in sails. Each cascade adds a multiplier to the points value at that stage. As such it is always a good idea (if you are able to) to add a non-box column to drop into the boxes to start. Even adding one of these doubles the score to that box.
Clearing the board all at once is flashy, but you don't need to. Keep to triples and bingos and you should do well (as long as the are ending in boxes).
It is useful to start filling from the bottom, but leave ONE piece empty from the box for you to have an overhanging piece from a higher box fall into (or a piece resting on it, or a piece from the "blank" bits in a box").
Gunning - Speed Puzzle
Tip 1) Look up "Looping" on youtube (search for somethign like "gunning puzzle pirates looping tutorial". A visual demonstration will be miles better than anything I can write.
Tip 2) Don't necessarily loop around all 4 cannons - smaller loops around 2 cannons can be much faster, especially if you are board sitting like you would with a sloop or a dhow.
Sf and rumble....
I thought about writing for this. My best advice for these puzzle, basically, is to go look up the rules for how the attacks are calculated I may write this as well later if I am bored.