Continuity mistake: When Lando says "Go on, you pirate" his entire outfit is reversed - his shoulder holster strap goes the other way, and his rank insignia changes side too. (00:50:00)
Factual error: Chuck Yeager's sidekick, Jack Ridley, appears in many key events which occurred after 1957, including the climactic 1963 test flight of the NF-104 plane that Yeager ejects from and is picked up by Ridley. Jack Ridley actually died in 1957, when the aircraft he was co-piloting crashed into a mountain in Japan.
Visible crew/equipment: Right at the start of the film as the alien spacecraft is landing on the planet, you can see the scaffolding of the studio at the top of the screen.
Factual error: The caption says "twenty years later" before the main part of the movie starts. Now judging by the dates we've seen on-screen so far that would be in the reign of William and Mary, not Queen Anne.
Factual error: In one scene, our heroes go down a water slide with their bikes. Landing in the pool at the end would have made their walkie talkies unusable. But later they still work normally.