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.]