During Professor Robinson's "Volta Blade" duel with the Leader, he splits a tree in half with his sword. One half of the large tree falls on the cord of his electronic sword, completely trapping it. In the next shot, the cord has come "untrapped" from the tree and is again swinging freely.
At the beginning of the episode Will and Dr. Smith are monitoring an intruder alert system, but in earlier episodes it is shown that the Jupiter 2 has a force field that can be deployed meaning that the intruder alert system would have been unnecessary.
The alien "fear gauge" meter, a DC milliammeter, has the words "Made In USA" at the bottom right of the meter face. Approximately 40 minutes in.
Around the 47 minute mark Dr Smith is painting. John Robinson take the painting off the easel to get a better look. When Dr Smith take the painting back and replaces it on the easel it is now rotated 90 degrees.