Continuity mistake: When the Jupiter 2 is flying it is a single level ship, when it is on the ground, its a two level ship and in one episode it was even a three level ship.
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.
Other mistake: Where is there enough space to store the rover and other vehicles on the Jupiter 2?