Factual error: Buck Rogers is supposed to be a Captain in the Air Force, but he is wearing Navy wings. In fact he is not even wearing Naval Aviator (pilot) wings, he is wearing Naval Flight Officer (navigator) wings.
Factual error: In the narration intro Buck's 1987 spacecraft is called "Ranger 3". But the Ranger series spacecraft were unmanned lunar landers, and NASA never repeats project names to avoid confusion.