Continuity mistake: When Sandy is waiting for the ferry, he is playing with his Gameboy. When he sees Flipper, and tosses the can in, you can see he is still holding the Gameboy. However, when Flipper throws the can back Sandy catches it with both hands and is no longer holding his Gameboy. After he drops the can, we see that the Gameboy is back in his hand.
Continuity mistake: At the end when Sandy is telling Flipper to swim away, it shows the top half of Sandy's body. One of his arms is on a rail on the side of the boat. It then cuts to show Sandy's legs and Flipper, and now both his arms are suddenly by his side. It cuts again to show his top half, and his arm is on the rail again.
Continuity mistake: When Sandy first comes to the island and goes to Porter's house, watch his shoes. When he is walking on the beach he is wearing white tennis shoes and still is when he knocks on the door. In the next shot when he plays three notes on the piano he has on black sandals. A minute later when he later walks out on the dock to find Porter he has the tennis shoes back on.