Executive Meddling: The original subtitle was "Triforce of the Gods," but it was deemed necessary to change this for American audiences in case any Moral Guardians threw themselves in a tizzy over the alleged references to religion and gods. Despite this, the American manual explicitly uses the term "gods" in explaining the game's backstory and Hyrule's creation myth.
Butter Sword: The Golden Sword, named so for its golden color.
Breadsmiths/Bakers: The dwarves who give you the tempered sword, named so because they look like they're hammering away at a loaf of bread.
The D: The Bow, named for its shape.
Hype Cave: A cave southeast of Link's house, named so because it is full of chests that often hold useful items when playing the randomizer.
The Lunch Box: The purple-colored locked chest that you have to bring to the thief near the desert in order to unlock.
Since Sahasrahla's name is difficult to remember, it is often spelled/pronounced incorrectly (either by accident or on purpose).
Spite Cave: A cave near the graveyard that is full of spikes.
Flip-Flop of God: At the time of this game's release, the back of the box said it was a prequel to the NES installments. The story told in the manual seems to reflect this, detailing the origin of Hyrule, the Triforce, and Ganon. By 1998, however, Shigeru Miyamoto seemed to have changed his mind, stating that it was a sequel, even though this makes almost no sense plot-wise and is now mostly seen as a slip of the tongue from his part. He gave another interview in 1999 that seemed to confirm the originally-intended order. Taken a step further when Ocarina of Time was made in 1998, which created even more Continuity Snarl (how it ends on both ways when the Adult portion ends and begins with Wind Waker and the other to Majora's Mask then to Twilight Princess). It wasn't until Hyrule Historia that the game took place after the defeat of Link, resulting in timeline number 3 and eventually, this game. It also did confirm it was a prequel to the NES game, just not to the series as a whole.
Urban Legend of Zelda: The game features one of the most famous non-gameplay related examples in gaming. At the start of the game, your injured uncle tells you "Zelda is your...". This has led many gamers to believe that Zelda is Link's sister (or more rarely, Link's cousin), and some believe the Japanese version made it more explicit. In the Japanese version Link's uncle says "Y-you are the princess'...", which has led fans to speculate that the line is actually something along the lines of "You are the princess' only hope" (though some still see it as "You are the princess' brother"). The GBA version of the game contains a new translation which says "You must rescue Princess Zelda. Our people are fated to." instead. Thus far, Link and Zelda haven't been been presented as related in any incarnation except in the first manga (which is full of Early Installment Weirdness, is an adaptation of the first title, and is non-canon to the games).
Concept art included in Hyrule Historia shows Zelda dressed in skimpy armor◊, which might have been the inspiration behind Sheik in Ocarina of Time.
An Animated Adaptation was in the works by Aeipathy Industries, but it was cancelled when they could not get the rights from Nintendo.
The game was originally meant to be sci-fi related, hence the aforementioned Zelda concept art. Link was supposed to switch between the current Hyrule and a futuristic version, instead of between Hyrule and the Dark World.