This is probably the most unknown sequel in Final Fantasy series since it wasn't released outside of Japan until 2006. This comment is based on a NES emulator translation of the original.
Story tells about four unnamed orphans who are sent to protect Elemental Crystals and the world from Xande's clutches. The structure of the plot is in like in first Final Fantasy, especially in the beginning it feels like pointless wandering in huge, maze-like, non-save point dungeons. From the middle game it's coming clear what is supposed to do to prevent world from destruction. Dialogue is often childish as are some events (adventure begins when the four orphans accidentally falls in some pit in a cave). Characters are distant since they are not met very often.
Other parts in Final Fantasy III work well. Monster design is unique and colorful. Music has it's moments, especially in the final place before fighting the last boss. Class system is interesting with classes that can be changed. Combat is simple and smooth. Most of the game player can go calmly to the destination, only in the very end is annoying "you must wander pointlessly so that you loser characters would have some chances to survive"-thing.
Overall Final Fantasy III is surprisingly smooth considering that is one of the NES Final Fantasies.