The title is a Biblical quote from Genesis 6:4.
While having Smith and the Robot stay behind is a way of emphasizing Smith's attitude of not helping the Robinsons, it was actually done for a more practical reason. The first several episodes of the show reused various parts of the original unaired pilot which did not have Smith and the Robot as part of the crew. By leaving them back at the spaceship they could save a lot of money not having to film new sequences and just reuse the old footage.
Leftover from the unaired pilot, a music cue from The Day the Earth Stood Still (1951) by Bernard Herrmann is used again during scenes inside the cave.
Will Robinson sings 'Greensleeves' at the campsite. 'Greensleeves' was the theme music for Lassie (1954) in which June Lockhart starred.