Dolphin trainer Ric O'Barry said on a few occasions he ran an extension cord down to the Miami Seaquarium so that the dolphins who acted in the Flipper TV show could see themselves when the shows they acted in screened on air. He said they were very self aware.
Luke Halpin as Sandy Ricks did all his own stunts throughout the Flipper TV series including the "Shark Hunt" show in Series 2 where he wrestled large nasty sharks to the surface caught on large hooks. The only exceptions were in "300 Feet Below" Series 1 and "Firing Line 2" Series 3 when the dolphin trainer Ric O'Barry doubled for Luke - the first being a 20 foot dive from a helicopter into the ocean and the second dodging stunt explosives designed to look like the skiff was being fired at by naval guns.
Flipper was played by three dolphins named Mitzi, Little Bit, and Mr. Gipper. Mitzi did the close-up shots, but she wasn't very athletic, so Little Bit and Mr. Gipper did the stunt work. All three were trained by Milton Santini, a commercial fisherman who started working with dolphins after accidentally injuring one in a fishing net.
The third show of Season 1 (SOS Dolphin) was filmed one year earlier (1963) as a pilot immediately after they filmed the last sequence for the second feature movie "Flipper's New Adventure" - Luke Halpin is wearing the same red t-shirt in the last scene of the movie and the opening scenes of the TV show.