When Dr. & Mrs. Bellows become invisible (due to drinking a magical wine), Major Nelson and Jeannie spend the entire episode trying to deal with the problem.
Yet all Jeannie had to do was blink the couple into their beds and make them fall asleep (or simply "freeze" them in place) until they became visible again.
This sort of thing is a frequent problem with "I Dream of Jeannie" (and also with "Bewitched"): the writers make the magical characters virtually omnipotent most of the time, but then make them unable to deal with even simple problems when it's convenient for the script.
For instance, on "Bewitched", it is shown more than once that Samantha can "freeze" people in mid-stride and keep them motionless until she chooses to unfreeze them, at which point they just start up where they left off, without even realizing that anything happened.
Now think about how many times on that show just "freezing" someone temporarily could have easily solved the problem at hand (such as when a visitor to the Stevens home is about to see something peculiar, and Darren & Samantha have to scramble to head them off).
Yet the writers conveniently forget that she can do this whenever doing so might interfere with the writers' desire to stretch out a simple problem into a 30-minute episode.
The same thing happens often with Jeannie, and this episode is just one example. It's hard to enjoy a plot when the simple solution to the problem is so obvious, yet the characters seem too dumb to think of it.