When Smith starts quoting A Tale Of Two Cities he picks up a glass of wine and holds it at chest height but in the close-up shot the glass is at head height.
Before Dr Smith steps over to the molecular transfer beam to appear before the Galaxy Tribunal of Justice, Mrs Robinson and Will are standing in front of the Jupiter 2, with the Jupiter 2, the Robot, and the entire Robinson family behind them. A few camera shots later, the background behind Mrs Robinson and Will changes to the perimeter fence.
The morning after the perimeter fence is in place, John, Maureen and Don are at the breakfast table. John makes a comment about Don not having breakfast and only one cup of coffee. If you look agree the table, Maureen is clearing two empty plates, Don just had his cup of coffee. Cut to a hungry Dr Smith who joins them. He makes a comment "I'll eat this if you don't mind Major" and helps himself to a full plate of scrambled eggs and toast, sitting right in front of Don.
The robot describes the operation of the alien device as using "ultrasonic radio waves" . But ultrasonic waves are sound waves or audio frequency and radio waves are RF or radio frequency.
They put themselves in a dangerous position to dig a hole under the fence for Doctor Smith to escape, but the rest of the fence shows a huge space under it, that anyone could easily slide under.
The number of footprints in the sand change as the perimeter fence appears around the Jupiter 2 to imprison the Robinsons (reflecting the work of the crew that manually put it up).
When Professor Robinson is connected to the memory machine, he testifies that something went wrong with the robot. Then the screen shows a clip from launch date of Will and the robot on the lower deck, but at this time the professor was on the upper deck, he could not have seen what happened below, and so he couldn't have remembered it.