The character model for the Dark One is the same as Dragoon from Dawn of Dragoon (1983). Only the colors have been slightly altered.
The rainbow effect and backgrounds seen when She-Ra and Hordak travel between dimensions were seen earlier in [Quest for He-man (1983)] and [The Return of Granamyr (1983)] and will be seen again in The Greatest Magic (1985).
The Dark Dimension was first mentioned in Daimar the Demon (1983), in which Daimar claimed to be it's king. His place now appears to have been taken by the Dark One, who calls himself Master of the Dark Dimension.
The animation of She-Ra falling through space is reused in a sequence of She-Ra falling towards a ship in Anchors Aloft: Part II (1985).
According to the original script, the furry creature that asks for berries is called a Moawser, and the creature with a jewel in it's forehead is called a Queeper.