When Dr. Smith attempts to contact the space probe (externally a recycling of the 1st alien ship the Robinsons encountered in S1 E2 "The Derelict," 1965) & later when he & the Robot are confronted with the "brain surgery" issue, he is claimed by both Will Robinson & the Robot to be "not a real medical doctor!" as well as a "quack" (Smith himself declares he is a "doctor of ... psychology"). Yet the saboteur was also the physician giving them their physical exams before they took off & had the skill & equipment to revive both Major West & Maureen from the freezing tubes - especially after her negative reaction.
When the 3 aliens are in the Jupiter 2 holding the wand over Will's face while he is sleeping, Will is laying there with his left hand closed next to his pillow. In the next camera shot, his left hand is opened and laying on his pillow.
The robot tells Dr Smith, Professor Robinson and Major West that he was programmed in pre-med courses at the Institute of Cybernetics for 2 semesters. Later on, he tells Will that he had 2 years of programming, which would be 4 semesters worth of courses at most schools.
Before the shuttle craft accidentally leaves the Jupiter II, the outside door slides across to shut Dr. Smith and the Robot inside. After they land Dr. Smith is shown opening the hatch like a door.
The Robot says he was trained in the finest medical school in the galaxy. How he would know that isn't explained.
It would not have been possible for the Robot to climb down the steps of the shuttle craft.
When the Jupiter 2 approaches the space probe (b&w footage of "The Derelict" S1 E2 1965), John Robinson says "I've never seen a spaceship that big in my life!" an expansion on what he originally declared, about "anything like that in my life." Since they had been out only 2 years - most of which was spent on the ground - this statement is highly exaggerated.
The young Dr. Smith talks with his adult voice. He should speak with the voice of a child.