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.
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.