Other mistake: One of the episodes shows John at a Marine base camp. It shows him wearing Army fatigues, and in Episode 7, Maureen jokingly says "weren't you a Navy SEAL?" right after he fails to throw this hook to get to safety from a tar pit. So what is he? A soldier? Marine? SEAL? Can't be all three.
Suggested correction: Navy SEALs will wear camo to disguise themselves.
SEALs are Navy. So John is a Navy guy in a Marine Corps base using Army fatigues? A bit messy I guess.
Military folks end up on various bases all the time. I was in the Navy for 20 years and found myself, at different times, operationally committed to being on Army, Air Force, Coast Guard bases, and plenty of other bases with Marine detachments, to say nothing of bases of foreign militaries overseas. If you happen to be on a joint operations base, like European Command, you'll see everything walking around. Not as odd as it sounds.
Danger, Will Robinson - S1-E10
Plot hole: At the end, when Maureen is searching for John in orbit, she only radios him after Will sees him clinging to the floating wreckage. Before that, she only used sensors aboard Jupiter to try and locate him. She makes no attempt at radio contact for any survivors, which would have quickened the rescue. John can also radio her back, but he did not attempt to call for help.
Suggested correction: The suit radios are fairly short range. This is seen on a number of occasions, such as when they need an extension antenna when stuck in the tar to contact others. The distances in space between the damaged Jupiter and Jupiter 2 are huge, and much further than the distance from the chariot stuck in tar back to Jupiter 2.
The Robinsons Were Here - S1-E4
Stupidity: Satellite dish falls, trapping people inside, and they can't even figure out a basic thing like digging a hole to escape. (00:43:52)
Suggested correction: I didn't see anything they could use to dig their way out. Plus Don was on the other side, so they knew they could just wait.