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.
Lost in Space (1965)
1 factual error in show generally
Starring: Guy Williams, June Lockhart, Mark Goddard, Marta Kristen
Visit to a Hostile Planet - S3-E2
Continuity mistake: When the guy shoots the Robinson Robot it leaves a big bullet hole on the front. In the next shot we see the Robinson Robot turning around and the bullet hole is gone.
Robot: My micromechanism thanks you, my computer tapes thank you, and I thank you.
The Great Vegetable Rebellion - S3-E23
Trivia: Due to their uncontrollable laughter during filming of the infamous "Vegetable Rebellion" episode, Guy Williams and June Lockhart were written out of the next two episodes.