During the scene with the children on the patio, the yellow tissue paper (that had wrapped the fire engine toy) was strewn around continuously appears and disappears (seen from the inside of the house, but alternately seen from the patio).
Haji indicates that Jeannie's parents would be devastated to learn that she was marrying a mortal. But in an early episode, it was revealed that Jeannie was born a normal human, until an evil Blue Djinn turned her into a genie and imprisoned her in her bottle. As such, Jeannie's parents would be mortals too.
In the second vision of the future, Hayden Rorke refers to Larry Hagman as "Major Nelson" in spite of the fact that the future Tony has previously established as being a colonel. Rorke then realises his mistake and fumbles over his next line.
This is based on the premises that Jeannie will loose her powers when she married a mortal. However, the characters should have know this from There Goes the Bride (1967) when Jeannie tries to marry Tony and Haji tells her the same.