Revealing mistake: Watch closely the two scenes involving the Robot; (1) When the Omega 17 IDAK battles with the Robot you will see pieces of his plastic collar continually. (2) After Verda and the Alpha IDAK disappear you will notice the Robot's lower shutter falls out.
Continuity mistake: In the exterior shot of the Jupiter II landing on the planet we see through the front window that there are 2 figures in silhouette standing at the control console throughout the landing. Upon touchdown the shot changes to the interior where John Robinson and Don west are sitting behind the console and are strapped into their seats.
Continuity mistake: When John is trapped in the electrical anomaly he tries to answer the radio and it is shown exploding. When Don and Judy start rescuing John you can notice the radio is still there, one shot with the antenna up and one without, and another with no radio.
Visible crew/equipment: When Will and Dr. Smith first come upon the Trader's encampment, just as the dogs start to attack you can see the head of a crew member (dog trainer?) bob in and out of view from directly behind where the dog on the right was lying...from behind the boxes stacked on the ship's platform. (00:08:38)
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.
Plot hole: The Jupiter 2 crew is duplicated; however, the aliens had never seen Penny (or Judy I think). How can they be duplicated? The aliens don't have ability to know who were there, or they wouldn't have questioned Smith about the crew. Also, they do not know Smith and Will are hiding. So, they don't arm to have any special power to know beyond what they actually observe.
Character mistake: Dr Smith who has some of The Robot (ie, bravery and courage) quotes The Fall of The Light Brigade but mistakenly says "into the valley death rode the five hundred" when it is actually 600. Both Dr Smith and the Robot would know this very famous poem's most well known line. (00:44:45)