When the boys and El (Millie Bobby Brown) are walking to try and find the gate, they walk along railroad tracks in pairs, in a scene very reminiscent of scenes from Stand by Me (1986). "Stand By Me" was based on "The Body" by Stephen King. King is a major influence on this series.
The teacher who explains the science behind the Upside Down to the boys is called Mr. Clarke (Randy Havens). His name may be an homage to science fiction writer Arthur C. Clarke, whose most famous novel adaptation, 2001: A Space Odyssey (1968), also contains a tunnel through time and space like Mr. Clarke describes here.
The acrobat can move forward and backward along the rope. But the flea can move forward and backward as well as side to side. If the flea keeps walking to one side, it goes around the rope and winds up where it started. So the acrobat has one dimension, and the flea has two dimensions, but one of these dimensions is a small closed loop.
So the acrobat cannot detect any more than the one dimension of the rope, just as we can only see the world in three dimensions, even though it might well have many more. This is impossible to visualize, precisely because we can only visualize things in three dimensions.
This is the first episode in which Eleven (Millie Bobby Brown), Mike (Finn Wolfhard), Dustin (Gaten Matarazzo), and Lucas (Caleb McLaughlin) refer to the alternate dimension as the Upside Down.
This episode takes place from November 10 to November 11, 1983.