Boober is plagued in his dreams by Sidebottom, his playful side that he keeps on the bottom. Boober tries to repress this dangerous, uncontrollable side of himself, so Sidebottom enlists Boober's friends in a bid for a permanent identity.
Fraggles can share each other's dreams. All they have to do is fall asleep with their heads touching and say, "Dream a dream and see / What a dream can be." Then they can enter one dream. There's even a whole song dedicated to the ritual.
A game the Fraggles play is Fraggle Freeze, their version of freeze tag.
Another Henson fantasy world makes a cameo in this episode -- in Uncle Matt'spostcard, he mentions visiting a drive-in, where The Dark Crystal is being shown. He sees a couple brief clips of the movie.
Doc reads in a dream analysis book that "...little creatures that high that are green and wear helmets are symbols of work and creativity." This is an obvious reference to the Doozers.
At the end of the episode, Doc refers to the Fraggles he saw in his dream as "silly creatures", the same term Matt Fraggle uses to refer to humans and most other "outer space" lifeforms. This illustrates the shows premise of how things are seen from different perspectives.