Big Nate Island
Scare the seagull away by turning the crank on the lighthouse with a lobster. You can swap the photo from the lighthouse for diving gear, and recover Cap'n Salty's lost lobster trap.
Astro Knights island
Get the Laser Lance from the jungle. Charge up the Laser Lance by holding your mouse button, then releasing it for a power shot.
At Parrot Port, get the cracker from inside the pub (upper left) and after you find the pirate, use the cracker to lure the parrot.
(see related questions)