Although it's established in at least 2 episodes that genies cannot be photographed, Jeannie's photo is prominent on the front page of the Honolulu newspaper.
This episode makes no sense being aired this early in the season. The three season 3 episodes in Hawaii were all filmed together. This one fits better for continuity watching it as the third of the Hawaii episodes, after the first two in mid-season.
In The Girl Who Never Had a Birthday: Part 1 (1966), it is established that Jeannie was born in 64BC. So her claim isn't possible that she knew King Tut and that he was fond of her and gave her the scarab. He lived over 1200 years before she was born (1342-1325 BC).
When Jeannie goes on the day trip she is wearing a aqua blue pants and stripped shirt but, but in the next scene at the helicopter she is completely in a different outfit.
When Jeannie pours out the 'diamonds', they already look like rock candy.