In the scene after Sandy leaves his home, he's supposed to be in the middle of the ocean, but in the opening shot, Flipper is seen swimming near a dock which can be seen at the top left of the screen.
When Sandy climbs up over the gunwales of the boat after tying the third escaped convict to the bow, he is almost totally dry. Yet seconds later, as he is untying the family, he is wet all over. In fact, as he climbs into the boat, he has a goofy grin on his face that he unsuccessfully tries to hide from the camera, probably because of the fact he isn't really climbing out of the water.
When Sandy is called over by Mr. Porett, he's holding a banana in his hand when he has his feet in the water. In the next scene the banana has mysteriously disappeared from his hand.
When Porter Rick's friend calls him at the ranger academy he is speaking with someone on the phone and tells them he needs to speak to Porter Ricks. He gets Ricks on the phone and later, at the end of the conversation, we see Ricks is in a phone booth.
Several scenes are reused constantly. This is evident in the final battle between flipper and the lead convict, when the scene of flipper going up to the camera and swimming away is used about 3 times.
In the scene where the second convict is collecting the drifting cans of food, a fence can be seen on the top of the screen.
When flipper flips the second convict's boat, he's swimming in deep water, but from the shot where he's flipped, it's obvious the water is waist deep.