Bad Export for You: The NES game is a great game in its own right, but the Famicom version has a better sound chip that leads to its music sounding a lot better, and Grant is a more useful character for combat as his basic attack is throwing his knife with no heart cost, instead of the stabbing attack with pathetically short reach he has in the NES version. The Famicom version is also significantly easier as covered on the main page, though that one is more a YMMV thing, as players may enjoy the greater challenge of the NES version instead, especially its boss battles that better live up to their name, and its second quest that provides a real Harder Than Hard mode for those seeking something especially challenging.
Fanon: Some previews in Nintendo Power and elsewehere lead to the impression that the three companions are ghosts, and when you hit select you're actually giving them control of Trevor's body. This does seem to make sense given that you defeat both Grant and Alucard in combat, and Sypha emerges from a petrified state. This is Jossed by the various endings of the game, however.
Saved from Development Hell: In 2006, Project 51 Productions acquired film rights to produce a straight-to-DVD animated film based on Castlevania III. Simply titled "Castlevania Dracula's Curse", it would have been written by Warren Ellis with art direction by James Jean. Since the project hadn't been updated since 2008, it was long presumed cancelled. It was finally released on Netflix as an animated series in 2017.