Continuity mistake: While the boys are trapped underwater inside the car, when Porter opens the jammed car door, his left sock is missing, but as he and the boys float up, Po's wearing both socks. (00:20:00)
Continuity mistake: Bud is lying on a surf board, talking to Flipper. During different camera angles, his position on the board changes. He goes from the middle to almost the top. At the end of the scene, in the wide-shot, he's always to the end of the board. He also goes from being centered with a foot on each side of the board to being on the left-side with just that foot in the water. (00:13:20 - 00:14:20)
Not Necessarily Gospel - S1-E7
Continuity mistake: Hap puts his hand around Bud's side. Camera angle switches, his arm is on Bud's shoulder. Another switch his hand is no longer on Bud. Camera angle switches once again and Hap's hand is being removed from Bud's shoulder. (00:16:39 - 00:17:00)
Continuity mistake: Aboard Tollner's boat, when Porter and Tollner are above the water, both of their gear straps are yellow. But while underwater, one of the men has dark gear straps. (00:15:00)
Flipper and the Elephant: Part 1 - S1-E24
Continuity mistake: Simpson is trying to pull a baby elephant onto his boat when the rope snaps, causing him to fall into the water port side. You can see the end of the broken rope going with him. Next camera angle, the rope is wrapped around the cleat and Simpson is being towed behind the stern. (00:18:55)
