While Dr. Smith waits for Penny's return to the lower level after sending her to reset the astrogator, the robot is seen moving slightly, even though Dr. Smith had removed its power pack.
When Smith pulls out the robot's power pack, the robot, rendered powerless, slumps over to its right; yet, when Smith sends Penny upstairs, the robot, still deactivated and powerless, stands in its upright position. Time passes, and the robot now appears slumped forward rather than to its right or standing straight.
After Major West retrieves Dr. Smith from the Green Lady's trance just outside of the Jupiter 2, both of their helmets are missing as they come back inside through the ship's inner hatch.
When Smith cries out "I got it," the Robot turns sharply towards him, but when the scene cuts to a wide shot, the Robot turns slowly towards him all over again.
The indicator lamp that originally showed "Robot Power" no shows "Fuel Jettison Activated".
Seductress Lorelei floats in space without any form of communication device. As sound cannot travel in a vacuum, it would be utterly impossible for either Smith or the robot to hear anything that she says.
After entering the solar system and passing by the sun, Maj. West does NOT say that their spaceship will pass by Uranus and Arcturus to reach Earth. He says "We should be able to see Earth by now passing by Uranus and Arcturus." Uranus is a planet in our solar system about 2 billion miles away whilst Arcturus is a colossal star over 200 trillion miles away. Don speaks of appearances, not actual distances.
The sun appears red and smoking, which it is not and does not. The smoke drifts swiftly, even thought the immensity of scale would cause any such emission to take hours or days to move from one part of the sun to another. Furthermore, it is all drifting upwards, even though there is no overriding gravity upon the sun from another body to cause it to move in one direction.
The first two exterior shots show the Jupiter 2 in sepia tone, suggesting it's archive footage from the first season in black and white. Later exterior shots appears blueish and/or purplish -- even kind of pinkish at one point.
In the opening teaser, John Robinson comments to Will that the ship is closer to two million miles out in space after leaving the planet, and Will exclaims that they must be traveling near the speed of light, which Major West confirms. If that's so, with light speed being ~186,000 miles per second , two million miles would be covered in a bit under 11 seconds - far too short a time for the scene.
If it would only have taken them 4 days to get to Earth (compared to 98 years to Alpha Centauri), they could have gone there to let everyone know they're OK, gotten repairs, and dropped off Dr. Smith, then taken off again. It made no sense for Dr. Robinson and Major West to insist on going straight to Alpha Centauri.
Both Dr. Robinson and Alpha Control keep saying the Jupiter 2 is headed out of the GALAXY instead of out of the SOLAR SYSTEM.