Factual error: Col Sinclair's service cap has six clouds and lightning bolts ("farts and darts"). That hat is for general officers. A colonel should have four clouds and lightning bolts.
Factual error: There are many Air Force uniform mistakes. Col. Sinclair has his pilot wings on the right chest instead of the left. He has enlisted "U.S." insignia. The Commanding General of the air base has his Brigadier General shoulder insignia on the edge of the epaulets. The Brigadier General star is worn centred on the epaulet.
Factual error: The weapon Palmer used to shoot down one of the enemy fighters was the M79 grenade launcher. This weapon's projectile speed is lower than the speed of the plane, so it would be impossible for Palmer to hit a target flying over 100mph side-by-side.
Factual error: The Me-263 was in fact a Rutan jet. Moreover, the Me-263 was only a rocket-powered project, while the most popular Nazi jet was the Me-262.
Factual error: Lou Gosset's character's uniform was REALLY wrong. He was wearing an officer's uniform with enlisted man's insignia on the lapels. [People try and argue that it's illegal to use a correct uniform in movies, but I've yet to see any concrete evidence of that fact - if anyone can provide a link to the law/rule that states that, please let me know.]