Goofs

When Tony finds Jeannie's in his office as his new secretary, she says, "Private Nelson" and points to her single chevron on her sleeve. Privates and Corporals were obsoleted in April 1952. Jeannie wears the rank of Airman 1st Class.

When indoors Jeannie salutes her superiors, but that is not what is reality in the armed forces. Only when outdoors is saluting required when passing a superior rank.

When Captain Nelson's new secretary introduces herself as "Corporal Burns" she is wearing a uniform with three stripes on the sleeve, i.e. the rank of an Airman 1st Class. Besides, the Air Force hasn't had the rank of Corporal since the early 1950s.

Captain Nelson turns Jeannie's Bottle upside-down before pouring water into her bottle. Jeannie fiddled with her hair unaffected by gravity shifting - let alone tossing her about in her bottle.

Had Jeannie canceled out the effects of forces on her bottle, water poured would never have reached Jeannie.

There are multiple references to "Lucas Air Base, North Africa", which never existed. The closest real location would have been Wheelus Air Force Bace. Libya.

Jeannie is accepted into Air Force Basic Training, despite lacking a birth certificate, high school diploma, etc. Further, she is later assigned to be Tony's secretary at NASA, without ever attending tech school, or getting a security clearance.

Upon learning she may not be able to remain as Tony's secretary, Jeannie wants to quit. Tony tells her the Air Force only lets "girls" out under a limited set of circumstances, failing to mention that a court-martial and a less than honorable discharge, would likely be required. Jeannie makes a mess of Tony's office, and that seems to meet his stated requirements for separation from the Air Force.