In the opening shot of the teaser, the stock footage of the jet landing is a two-seat F-106 Delta Dart trainer. In the taxiing shot, the plane is the single-seat variant of that aircraft. Later, when Tony and Roger are on their way, the stock footage shows the two-seat F-106 trainer again. Good choice since there are two seats! But the shot of them landing is the predecessor to the 106, the single-seat F-102 Delta Dagger. No room for Roger there.
Roger Healy's suitcase has the letters USAF stenciled on it. This stands for United States Air Force, but he is supposed to be an army officer.
Major Healy's hat has a plain black visor. In the Army the ranks of Major and above have the gold "scrambled eggs" on the visor. Lieutenants and Captains have the unadorned visor on their hats.
Wardrobe mistake! From this point on, even though Tony was promoted to Major, he continues to wear the company grade service cap with the plain brim. An Air Force Major wears the field grade service cap with the decorated brim, the same style that Dr. Bellows wears.
When recently promoted Majors Nelson and Healey rendezvous at Tony's house before leaving on their trip, they are each wearing their new rank insignia: the oak leaf cluster of a major. However, while Roger's are the correct color (gold), Tony's are incorrectly colored. Tony's are silver. A silver oak leaf cluster is the rank insignia of a lieutenant colonel. However, since this was shot in black and white, it is possible that this is not an error on the part of the show's producers, but rather an error made by the decades-later colorizers of the show.
On one of the rolls at the crap table, one of the dice clearly has two faces with four spots on each of them.
Nellis Air Force Base is Las Vegas. Reno is a long way from there.
Major Healy is in the Army, but when traveling to Reno, his bag says U.S.A.F.