Factual error: The Robinsons exceeded the speed of light due to impurities in chemical rocket fuel. No chemical rocket fuel comes remotely close to the energy content needed to even approach the speed of light. That would require exotic fuels like antimatter. By Einstein's theory of Special Relativity it is impossible to exceed the speed of light with any form of rocket propulsion. Faster than light travel and time travel might be possible with the warped spacetime of Einstein's general theory of relativity and phenomena such as wormholes. For plausibility the opening scene should have been an encounter with a wormhole.
Factual error: There's an exhibit in the Smithsonian Institute that shows Benedict Arnold, William Demont, and Major John Andre labeled as Famous American Traitors. One problem, Andre wasn't a traitor to America as he was a British officer to whom Benedict Arnold arranged to surrender West Point to during the war.
Factual error: As the robot bird approaches Earth, South America is the wrong way around.
Factual error: Shannon asks Leah if she knows what happened to Tom Smith - she replies that Tom has gone to university, but in the previous series Tom was only in his first year of sixth form, and it takes at least two years in the sixth form to study for the A levels required for a university place.
Suggested correction: Although normally A-levels are taken after 2 years, it is possible (and often done) to study them in one year.