The game borrows very heavily from the tabletop game First Edition Dungeons and Dragons. The list of monsters to fight is nearly identical to the bestiary from that game. The possible character classes are similar (Fighter = Fighter, Black Belt = Monk, Thief = Thief, White Wizard = Cleric, Black Wizard = Magic-User). The magic system is similar, with many analogous spells and the same level-based spell charge system.
In the 1990 NES release, you could obtain a world map by pressing B and Select at the same time. This is a hint given to you early on in Matoya's Cave; take what the brooms have to say and spell it backwards.
The Nintendo Power strategy guide for this game stated that certain weapons did additional damage to certain enemies (Coral Sword vs. water enemies, for example). This is not true in actual gameplay. It is not clear whether Nintendo/Square intended to actually implement this and forgot, or whether the Nintendo Power information was completely fabricated. (Note this only applies to the original NES version; these weapons perform their intended effects in subsequent versions of the game)
Along the same lines, there are certain spells that do nothing at all! These include the Black Magic spells TMPR, SABR, and LOCK. LOK2, a supposedly more powerful version of LOCK, in fact does the opposite of what it was intended to do--it makes the enemies harder rather than easier to hit. (These bugs apply only to the original NES version; these spells perform their intended effects in subsequent versions of the game (Wonderswan Color and Game Boy Advance)
Nintendo Power ran a contest in which the object was to obtain a photograph of a battle screen on which WarMech was shown. WarMech is an enemy that appears randomly and very rarely along the long bridge leading to Tiamat in the Sky Castle. He is very difficult to defeat and can't be escaped. It is believed that WarMech started the tradition of placing very difficult but optional enemies towards the end of a Final Fantasy game.
Fire, earth, air and water are the Classical Elements, which were believed by the ancient Greeks to be the constituents of the universe. However, the concept of classical elements likely began earlier. A fifth element, "aether" was added to describe stellar objects. The Hindus also had the same concept of classical elements.
Likely a programming glitch, there is an invisible woman in Coneria Castle.
Arylon the Dancer, the price of the Power Staff, and the tombstone of Erdrick are intended to be answers to questions in a sort of "scavenger hunt" contest by Nintendo Power that appeared shortly after Final Fantasy came out in the U.S.
Erdrick is the hero of legend in Dragon Warrior, explaining how his tombstone showed up in another Nintendo-produced game. In the Japanese and Dawn of Souls versions, Link (of Legend of Zelda) was the name on the tombstone.
The humor website Seanbaby.com named the AMUT spell one of the "Most Useless Powerups in Video Game History", along with such classics as the Feather from Milon's Secret Castle and the Cloak of Invisibility from Wizards & Warriors. Contrary to what is implied by the article, there are enemies that use the MUTE spell in the game, but they are so rare as to make an anti-MUTE spell useless.