Carp scoring
The values used in this article are for the purposes of demonstrating relative values only.  
The actual mechanical values behind the puzzle are undisclosed. 
Contents
Basic points
Points in carp are scored by covering bare holes. A plain piece played scores 10 points if all 5 spaces are empty. Counting each piece played as a cost of 10 gives a base 100% efficiency for placing pieces in a hole with no overlap and not finishing holes.
Uncertainty and history of point discussion on the forums
In the past, on the forums, the score has been counted as 1 points per space covered. This, however, results in fractional points. The scoring numbers shown here are based on pure integer math.
Hole finished factor
Completing a hole gives a bonus based on the hole size and the quality of the finish.
The bonus factors:
 A Masterpiece!: 2
 Craftsmanship!: 1
 A Fair Job: 0
 Sloppy Work: 1
 A Pig's Breakfast!: 2
This factor is multiplied by the number of pieces needed to cover the hole.
Example: A hole with 50 spaces takes 10 pieces to cover. An MP will score a total of 100 points for coverage, plus 20 points bonus, for 120 points.
Note that a really bad hole, when completed, will have a penalty.
Nice Set and Grain bonus
Grain bonus gives a one category bonus (+1) to the multiplier. Nice set is believed to also be a +1 bonus.
Chain factor
Multiple MP's in a row score more than a single MP. The exact score of this bonus is not known, but is believed to be another +1 bonus for MP's after the first.
Unknowns
 The effect of a wasteful (loss of a piece)
 The effect of a hole expanding
 The exact nature of the consecutive MP bonus.
Sample effective scores
Scoring in carp requires taking into account the need to play in all 4 holes.
Initial hole sample.
To fill an initial hole of 40 spaces (8 pieces) will take 8 turns. It will be necessary to play in all 4 holes to prevent waste; this means 11 pieces will have to be played. Assuming perfect play, this is 110 points, plus an 16 MP bonus, for 126 points, or 114% percent efficiency. A craftsman score would be 12 turns, and 8 fewer points (118 points), for 98% efficiency.
High score on carpentry requires that the first hole be an MP. Simply placing pieces into the holes to start will maintain 100% efficiency, but anything other than an MP for the completion will not give enough of a bonus to generate a sparkly hammer.
Long term example
Longterm MP scoring will score 10 points per piece, and 3 points per piece for the MP bonus; this is 13 per piece played, 130% bonus.
For anything less than MP, the scoring will depend on the size of the holes.
Assuming a 45 space hole (9 pieces to fill), and 10 piece filling (craftsman), this will score 90 points for the hole, and 9 points for the hole completion bonus; this is less than 100% efficiency. In general, in such a case, a hole of N pieces will score 11 * N in N+1 turns; the smaller the hole, the bigger the penalty for a craftsman score.
Duty puzzle scoring  

Important disclaimer: All point values used within these pages reflect relative values and weights as determined by players. No developer has commented on the current accuracy of any of these. Any forum post from developers that gave point scoring information is from prerelease days (preMidnight), and potentially has been changed. In particular, sailing (at least) has been known to have had major changes to scoring at least once. Use at your own risk. Past performance is no guarantee of future potential. Scoring may be changed in any update. Star levels do change the challenges that you face, and may change the scoring; the same play at different star levels may score differently. While this is known to be true in bilge, it potentially may be true in any puzzle.