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.
Other mistake: Where is there enough space to store the rover and other vehicles on the Jupiter 2?
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.
The Reluctant Stowaway - S1-E2
Continuity mistake: The Robot's legs move like a walking human. In later episodes he has treads.
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.
There Were Giants in the Earth - S1-E5
Revealing mistake: The Robot's lights wink out for a few seconds as it disables the force field.
Revealing mistake: When building the shelter, it takes both John and Don to lift the supposedly heavy panels; however when upright the panels bend easily when gripped. Obviously some sort of styrofoam/aluminium foil prop.
Other mistake: In one of the opening scenes with Will and Dr Smith, the Robot's power pack is clearly missing.
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)
Other mistake: When Don and Dr Smith are stealing Sesmar's control unit, look closely at the base of the electronic arch - Raddion is hidden from sight but the careful eye will see his golden feet.
Revolt of the Androids - S2-E24
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.
Revealing mistake: When the family are in the tubes so duplicates can exist, you can see some movement. Dr Smith blinks noticeably.
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)
Suggested correction: There's nothing to suggest they would know the poem exactly, especially since you yourself don't even know the actual name of the poem. It's "The Charge of the Light Brigade."
Continuity mistake: When Dr. Smith closes the door at the end when rehearsing the play, his cape is caught in the door. When the scene cuts back to the door a second later it is gone.
Revealing mistake: When Will looks through a window of the prison spaceship they crash landed on, a prisoner's hand moves on the staff he's holding, but he is supposed to be frozen and unable to move. (00:32:10)
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.
Visit to a Hostile Planet - S3-E2
Factual error: On the MTG radio broadcast the announcer states it is 3:15am on Saturday, 17 October 1947. 17 October 1947 fell on a Friday.
Deadliest of the Species - S3-E11
Other mistake: When the Robot is returning to his beloved with the energizer, he gets near the right side of the shot and abruptly vanishes rather than rolling off camera normally.
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.
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.
