The final boss of each chapter has in Japanese a variant spelling of the name of the last boss of the game, Odio, even trough it's less evident to notice that in the English fan translation of the game.
Most RPGs typically either a silent protagonist (who never speaks, only the player have to select 'Yes' or 'No' or equivalent answers) or normal protagonists where the hero have dialogue with other characters.
Live A Live is the only known game to that actually have mixed bag of both : The ninja, Sunset, Cube and Orsted are silent protagonists, while the other playable characters are regular protagonists. (there is also Pogo who speaks with jests and images instead of text, but that's still having an interactive dialogue so it doesn't count as a silent protagonist)
While starting a new Captain Square's game in the sci-fi chapter, it's written (c) 2099 Arumat Soft
If you reverse the word "Arumat" you'll found "Taruma" which is an actual corporation (http://www.tamuracorp.com/)
The old master in kung-fu chapter is called Roshi; this is the Japanese pronunciation of the name of the great Chinese philosopher Lao Zi (Lao-tse).
"Live a Live" contains some nice references to Latin language. The space ship in sci-fi chapter is called "Cogito Ergo Sum"; it is a famous phrase of the French philosopher René Descartes, and it means "I think, therefore I am".
Odio (the name of the Demon King) is also a Latin word, meaning "hate".
The Bakumatsu (ninja) chapter of "Live a Live" is based on a real historical event.