The air to ground (land mattress), air to air missiles (R4M), and the Luftwaffe jets actually existed at the time, were being tested, or being built within a couple years of the date the story takes place.
There was purposely a "Quantum Leap" element added to the story to give it more surprises and the actors state their surprise several times.
The Me 262 did not have its first flight until April 8, 1941 with 12 cylinder reciprocating engines, months after the movie timeframe. The jet engine was not delivered until November 1941. Hitler wanted bombers, not fighters, so this plane was only available in limited numbers in any model by the end of the war. Chuck Yeager now GEN(RET) shot one down with his P51 Mustang.
Everything that happens to the 757 keeps restricting her altitude and speed so the Luftwaffe planes could reach and keep up with the 757.
The 2 U.S. Army soldiers wearing Army Combat Uniform camp pattern are wearing the subdued US flag patch with the blue field on their left shoulder with the flag flying forward. In reality the flag is worn on the right shoulder with a reversed field to keep it flying forward.