When Raven is dancing in the Pandora story she tells, music from "The Overbite" is reused.
Starfire's smirk after her cheesy touch version of the King Midas story might hint that something terrible did happen to the king after he/she continued to consume excessive amounts of cheese thanks to the cheese touch...
Raven's Medusa jumpscare in Beast Boy's story was cut in the Philippines broadcast due to the executives believing that it is too scary for younger demographics.
Raven's hair turns into snakes in the story Beast Boy tells, which is a reference to Medusa.
Starfire's "Cheesy Touch" is a reference to the Golden Midas Touch.
Starfire did the "Floss Dance" in this episode.
The segment of which Beast Boy (as Icarus) had his shirt (made by his dad) that had a "Fly" tag labeled on his belt and then got severely burned is a reference to how the real Icarus ignored his dad’s warning of never flying too close to the sun; the shirt is the equivalent of the man-made wings of the myth of Icarus, which is also highly flammable.
Four Greek myths are being referenced and parodied in this episode:
It is unknown why the fairy in the Cheesy Touch story told by Starfire remains levitating after she gets turned into cheese, as cheese has weight and therefore should succumb to the forces of gravity.
Beast Boy should have been turned into stone after seeing Medusa Raven, as Medusa has the power of petrification with her snake-hair.
When he is dressed in a toga, Robin still wears his mask.
Starfire (as King Midas in her story) turning everything into cheese and eating them.
The Titans eliminating Robin when he's about to tell his story before telling their own.
The Titans calling Robin a goat man.
The transcript for "Don't Be an Icarus" can be found here.
The image gallery for Don't Be an Icarus may be viewed here.