After Smith pours the hot drink he lets go of the pot as he sits down but in the next shot his hand is still on the pot's handle.
A shot of Smith turning from the window and saying "Robinson alive? Impossible!" is reused from Island in the Sky (1965). However, when previously used, Smith was turning to talk to the robot. This time, Smith is alone in the ship and there's no one there for him to turn to. In addition, Jonathan Harris's costume changes from the turtleneck worn previously in the episode to the jumpsuit he wore earlier in the series for this shot only.
After the Robinsons, Don, and the Robot survived the earthquake and the super-hot sun, they headed back to the Jupiter 2 in the chariot. OK, fine. Yet, it is unclear as to why they appeared in their parkas once again while struggling in the non-frozen turbulent sea.
Battling the raging sea on the Robinsons' and Don's return to the Jupiter 2, Don climbs atop the chariot to repair the loose connection to the solar batteries. It is unclear why everyone is seen wearing their parkas... they had removed them prior to the earthquake and the super-hot sun attack.
As they escape the raging sea where everyone was wearing their parkas (a separate continuity issue), the Robinsons and Don find dry land. Yet, no one is wearing their parkas, rightfully so.
If the Jupiter II couldn't keep one person warm with temperatures of -120 Fahrenheit, how could it keep them warm in the cold of deep space?
Above Goof is in error because, when in space, the ship is powered including the HEATING and COOLING systems. The ship on PrePlanus is pretty much non-functional.
Will says "We might be on Cerberus." Cerberus is not a planetary body, it's a 17th century constellation (in the modern nomenclature of constellations, Cerberus' stars are part of Hercules).
A planet orbiting close enough to its sun to show the kind of motion depicted at aphelion would be close enough to experience temperatures far in excess of human habitability, shelter or not. The full orbit, as described by Professor Robinson in the diagram he draws in the sand, would result in a planet incapable of sustaining Earthlike life, plant or animal. Furthermore, the planet could not move fast enough in its orbit to go from deep freeze to oven in so short a time.
It is impossible that the Robot could play the guitar with 2 claw hands. Perhaps the claws could hold a pick for strumming, but fingers are necessary to hold the strings down to play chords.
Back at the Jupiter II, Smith is worried about freezing to death as the temperature drops, so why didn't he embrace that idea? He could have had the Robot put him into one of the hibernation tubes and freeze him in a way that he could be revived when the temperatures returned to habitable ranges.
The robot is playing the guitar which is an acoustic guitar, but the sound is that of an electric guitar.
While traversing the frozen sea, the temperature falls as low as 125 degrees below zero Fahrenheit...yet, despite there being six people in the chariot, there isn't any frost or condensation on the windows.
When the chariot is traversing the stormy sea, there's lots of thunder but little in the way of lightning flashes.
The robot is nowhere to be seen in the chariot as the Robinsons return to the Jupiter 2. Yet the robot is back in the Jupiter playing guitar.
A planet with an orbit such as Priplanus' which varies from extremely hot to extremely cold would most likely not support nor sustain the varied life forms shown such as turtles, chimps and ostriches. Of course, giant cyclops are another matter.
When Major West is washed off the roof of the chariot, the shots showing him hanging on the ladder; however, since the body of the entire vehicle is transparent, he should have been visible to the passengers still inside.