Just before they take off, Dr. Smith & John Robinson have a little talk about the Jupiter 2's destination, which Alpha Centauri having been the original intent John wants to continue their journey there. Smith bemoans, "We can't even be sure it's habitable!" to which John replies, "I'm well aware of that, Doctor." This runs completely counter to what was reported in the series debut, which was that Alpha Centauri had been "conclusively established ... as the only one within range ... able to furnish ideal conditions for human existence." It would be a titanic waste of resources & suicidal folly - both for the ship's company as well as the teeming billions "on our desperately overcrowded planet" to embark a colonization mission to someplace beyond hope of help that was anything less than certain of accomplishing its goal.
When the Jupiter 2 at last lifts off from the planet's surface her 3 legs/stairsteps are retracting into the hull, which when she first crashed (S1 E3 "Island in the Sky", 1965) they were not extended, after the fashion of a plane's landing gear, which had that been the case the legs would all have been completely destroyed on impact - & certainly there was no way to extend or use for the legs once the Jupiter 2 was flat on the ground.
The astrogator, which had been absent from many episodes leading up to series 2, has reappeared as the Jupiter 2 leaves the planet. In other episodes furniture and tables were present on the main deck of the ship in place of the astrogator.
In the prologue, Dr Smith's monument has an orb in hand and a plaque hanging from the statue's right arm/wrist. After the blast shock, Dr Smith replaces the orb in the hand of the monument. After the intro, the orb hangs from the hand (rather than resting in the hand) and the suspended sign from the wrist is missing.
At about the 33 minute mark the "Pyrex" brand name was visible on one of the flasks of "cosmonium" that Dr. Smith got from Nerim. Since Nerim was from an alien planet, this would not be possible.
When John flies over the weather station area to search for Will and Dr. Smith, he uses a hand held radio to call Will and Dr Smith. The jet pack uses two hand controls for navigation; it would not be possible to use one hand with the radio without loosing control of the jet pack.
The footage of Nerim's ship taking of was used several times before for different ships.
As Judy and Maureen are carrying off sporting equipment from the Jupiter2 to lighten the load for lift off, Judy comments about not realizing how much stuff has been accumulated until you have to get rid of it. Maureen replies the inquisitive instinct is still with us. All of this stuff would have been part of their original payload when they left Earth and not accumulated as Judy's comment implied.
It logically follows that Mr. Nerim's actions must cause the genocide of the society from The Lost Civilization (1966) including Will's friend the little Princess, yet none of the Jupiter 2 crew mention or seem the least bit disturbed by this horrifying fact.