Pull aside the white curtain to the right of the TV to find a bunch of cubby holes for all of Tumi's dog toys. Man, that's a dog with a LOT of toys.
The "Toy Clues" page you picked up from the table in the captain's quarters appears on the left, and now it's clear this is a logic problem; you have to figure out where to put all the toys based on those clues. Read to the end of this hint for the solution.
Each row and column has two of each toy: two dogs, two puffins, and two ponies. Pick them up from the top and drop them in the boxes where you want them to go.
The best way to handle this type of puzzle is to go down the rows one at a time (clues 1-6 at left) and place any toys you can.
Next, go through the columns (clues A-F at left) and do the same.
Now that you've placed a couple of toys, go through both lists again. Some placements will be possible that you couldn't figure out before.
When you've done that, it's time to start looking for rows with 5 of the 6 spaces filled; the remaining toy is now obvious.
The solution is actually the same for the amateur and master games, though the master game has harder clues.
This gets you a series of notes between Magnus and Dagny. Among other things, it tells you that Magnus had Dagny make a rawhide dog toy (made of rawhide so Tumi wouldn't chew on it) that locks with a key. How weird is that?
Dagny says she hid the key under the dog bed on the ship; next time you go there, look in the captain's quarters for it. There's no word where the toy itself is, so we'll just have to keep an eye out for it.
It also says that Magnus intended to look for something at the docks by scraping away the barnacles. You may have seen something covered with barnacles --
-- if you tried to take out the dinghy at low tide. If not, the next time you're in town, change the tides and go look.