Roger accidentally finds out that Tony has been replaced by a double and races to Tony's house to prevent the double from not only marrying Jeannie, but to prevent Doctor Bellows from finding out about her. They are successful on both fronts, but still have no clue as to where the real Tony is. However, it is revealed that the impostor Tony is also a double agent working for a foreign power sent to steal the project the real Tony was working for. Things really get complicated when the real Tony returns home.
People start visiting the house after Jeannie puts up a 'for sale' sign because she wants Tony to spend more time with her. Tony says that he doesn't want anyone else to see that house so she makes it invisible.
When Tony and Roger are trying to make a spacecraft fly, Jeannie does it with one blink. Tony tells her to get rid of it so she gives it to a boy in the park that has an inventor father. Tony gets accused of selling government secrets.
Both Tony and Jeannie are trying to play matchmaker with single Roger. Tony tries to match him with General Schaffer's niece, who turns out a big surprise, and Jeannie tries a computer dating service, which also turns out unexpectedly.