The shoulder boards on the General go from tucked below the collar to above the collar during his tirade.
Allison Ng puts her helmet on and the visor is shiny but in the next edit she has the leather protector on and has to remove it to reveal the shiny section. Allison then has her hands clearly up towards the helmet area but in the next shot her hand are down right before she gives the "hang ten" sign.
In the old footage at the beginning, President Dwight D. Eisenhower is signing the papers accepting Hawaii as a state. It was the 50th state but the sign seen in the montage said 49th state.
Despite seemingly having training in both satellite and space systems, neither General Dixon or Captain Ng wear the USAF Space Operations Badge.
USAF personnel are shown outdoors in uniform but not wearing hats. Regulations require all service personnel to wear headgear ("covers") outdoors, which must be removed when indoors. However, when USAF personnel are located on the flightline (aircraft operations area), the wear of headgear is strictly prohibited as they could easily be ingested into aircraft intakes causing major damage to engines and other mechanics. In addition, base commanders have the authority to declare a "no hat/no salute" parameter for celebrations/receptions on the flightline even if nearby aircraft are stationary and powered down.
In the Officer Club scene, the Senior Master Sergeant dancing is wearing officer cutouts (the little silver "US") on his lapel. As an enlisted man he should be wearing cutouts with a silver circle around the US.
The General makes reference to "Equatorial New Guinea," combining two different regions of Earth. Equatorial Guinea is on the west coast of Africa, and Papua New Guinea is just north of Australia. Papua New Guinea is just south of the equator and Equatorial Guinea is just north of the equator.