Every alien shown in the series is conceptualized by a different artist, as Shin'ichirô Watanabe intended to showcase the diversity and variety of alien species in the show.
No instrument invented after 1984 was allowed on this show; it was a full jazz orchestra working on the music.
In the world of the series, everyone still listens to music on audio cassettes. Mp3s and CDs do not exist.
Dr Gel is an evolved simian whose spaceship the Carnegie Lemon resembles the Statue of Liberty. This is a homage to the "Planet of the Apes" film series, which featured advanced apes and an iconic scene of the wrecked landmark.
The closing song mentions the name "Everett". This refers to Hugh Everett III, a quantum physics expert who brought up the many worlds theory of alternate universes. In the context of the show, this points at the episodic adventures Dandy goes through.