The Night of the Arrow - S3-E16
Factual error: The soldiers toss Artemus into the cell, slam the door and walk away. But they never produce a key or lock the cell door. He's somehow locked in anyway, though. (00:24:30)
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.
Sucker Bait - S1-E7
Factual error: It is quite true that atoms that do not occur naturally are bad for humans. However, in a space age as this story's, that would apply to most or even all planets. It would be a well known risk that didn't require an abnormal specialist to diagnose. (This fact rarely figures in other SF, because it would severely limit most stories).