Originally, the translated script of the DS version of IV was simply going to copy and paste the English script of the Game Boy Advance version with some alterations. Translator Tom Slattery, however, was a huge fan of the original game and offered to translate the entire game from scratch, making it more accurate to the original Japanese text while also using some modern series terms (such as "Eidolons" for the summon monsters.)
Contributed by MightyKombat
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In all versions of the game there is a secret passage in Cafe HOWDY!/Pub Lali-Ho in the Dwarven Castle of the Underworld that leads to a place called the "Developer's Room". In it are recolored sprites that are meant to be the developers of the game. In the DS release, it has the developers of the DS remake instead. This area was cut in "Final Fantasy 4 Easy-Type" and "Final Fantasy 2 (US)" because it's possible to find a pornographic magazine in the room, called Lustful Lali-Ho.
Contributed by Cavery210
Final Fantasy IV contains several prominent references to the Old Testament, such as the Tower of Babel.

Kain's name comes from the biblical tale of Cain and Abel, in which Cain becomes jealous of Abel and kills him. This parallels the multiple times that Kain betrays Cecil and attempts to kill him. Kain's ultimate weapon is Abel's Lance, alluding to the reference.
Contributed by SonicManEXE
The spells Protect (Armor), Shell, and Dispel were all cut from both the Easy Type and Final Fantasy 2 releases. Protect and Shell are still used by the Zemus Mind enemy, but the white magic icon was removed from their names, masking the fact that they were originally available to the player.
Contributed by Cavery210
In the original SNES English release, the Cockatrice/Cocktric summon is dummied out of the game for reasons unknown. Its name, like many other dummied out items within the game, is "Dummy" in both the summon spell and the item it was learned from.
Contributed by Cavery210
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In the SNES version of Final Fantasy 4, Tellah was mistakenly described as Edward/Gilbert's father. This was a translation error, and fixed in later releases.
Contributed by Cavery210
Edward is seen with a lute in Yoshitaka Amano's artwork and in the opening cinematic in the Final Fantasy IV DS remake, while in the game itself he plays a harp.
Contributed by Outofmind23
In the original Japanese release, the Cave Magnes/Magnetic Cavern/Lodestone Cavern/Cave of Power is darker. In the Easy Type and English releases, the cave was brightened up quite a bit.
Contributed by Cavery210
Nearly all of the items that could invoke magic spells were made inaccessible in the western release titled Final Fantasy II, as well as the subsequent Japan-only Easy Type release. Still retained were the FireBomb/Red Fang and the Lit-Bolt/Blue Fang, which are shown in the opening demonstration battles. The Lit-Bolt/Blue Fang item cannot be found in the game itself, however. Additionally, all of the items intended to cure a single status effect were also been made inaccessible, replaced by the Heal/Heal-All Potion, which was made cheaper in stores. Many treasure chests, shop inventories, and monster drops were modified to remove these dummied items.
Contributed by Cavery210
In all of the SNES versions, it is sometimes possible to open the menu while walking between tiles on the world map. If a Tent or Cabin is then used from the menu, it triggers the "sliding glitch." The map's collision will be shifted one tile away from the direction the player was walking. This by itself is cosmetic, however saving and reloading the game will reset the collision to match the graphics. This means the bug can be used to bypass certain map triggers or other impassible areas. This was fixed in the PlayStation version - it is no longer possible to open the menu when moving.
Contributed by Cavery210
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It's possible for certain copies of Final Fantasy IV to freeze if the player goes back and forth between doors 64 times. Square's defunct newsletter, "Ogopogo Examiner" wrote this glitch off as a trap created by Zeromus.
Contributed by Cavery210
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While Kain cannot cast any magic in Final Fantasy IV, the data in the SNES version contains a two-frame animated sprite for Kain casting spells, as all other spellcasters have. The Final Fantasy IV Settei Shiryou Shuu shows a screenshot of Kain with a White Magic command, and there is an unused empty magic spell list that, based on the internal character order, was intended for him.
Contributed by Cavery210
There is an unused 2-handed Ragnarok/Crystal in the item list within the game's data. It does not have a sword icon, but is named "None" (or "Spare" in the original Japanese version). If force-equipped to a character with a cheating device, its weapon graphic is the same as the Ragnarok sword and its attack and sound effect are also the same. It also has the same Holy attribute with an attack power of 200, the same attack power as the single-handed Ragnarok. The only difference is that it cannot be equipped by anyone. This sword is by no means obtainable in any version of the game, and it is found in all versions of Final Fantasy IV, including Final Fantasy IV: The After Years.
Contributed by Cavery210
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FuSoYa is the only party member whose in-game portrait has him facing to the right. Everyone else looks forward or to the left. He is also the only character in The After Years not to get a new portrait, with the exception of the portraits for the characters in their Pig or Frog status.
Contributed by Cavery210
Golbez's HP in his and FuSoYa's battle against Zemus at the end of Final Fantasy IV (2,943) can alternatively be read in Japanese as 憎しみ nikushimi, which means "hatred", while his starting HP in The After Years (2,971) can be read as 償い tsugunai, meaning "atonement".
Contributed by Cavery210
The CaveToad/GiganToad was renamed to 'Frogger' in the Easytype version of Final Fantasy IV, which was exclusive to Japan. It is a reference to the popular arcade game.
Contributed by Cavery210
According to executive producer Takashi Tokita (scenario writer of the original release), 3/4 of the original script had been cut from the Super Nintendo release due to hardware limitations, but some of this lost material was reworked into the DS remake.
Contributed by Cavery210
In the Japanese release, Edward and Golbez are named Gilbert and Golbeza. This was changed when being brought over to the US due to playable characters only being able to have 6 letters in their name.
Contributed by Cavery210
In the iOS port of the game, Cecil is introduced as "Load Captain Baron Red Wings" instead of "Lord Captain".
Contributed by Outofmind23
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The final boss, Zeromus, had a complete redesign for Final Fantasy 4 Easy Type. He was also made a lot harder, such as using Big Bang at the start of the battle. Zeromus EG in the Game Boy Advance and PlayStation Portable version is based on this version.
Contributed by Cavery210
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In the Japanese version each character had multiple abilities, some of these abilities were cut in the American version and the Easy Type versions for being less useful in battle than other abilities.
Contributed by Cavery210
In the final battle against Zeromus, Edge can steal an item known as Dark Matter in the Japanese version of Final Fantasy 4. This item, long thought to reduce the damage of Zeromus's Big Bang attack, is actually a joke item. In the DS version, a superboss named Proto-Babil appears if you use this item on the face of the Moon.
Contributed by Cavery210
In the version 1.0 release of the game (which only exists in Japanese), there was a bug that occurred when exiting certain areas of the game that messed with the game's RAM address of which location the player was in. Due to this, when exiting certain dungeons and then flying to the underworld, the game would think you were inside a lunar dungeon and read from the wrong set of enemy AI tables when entering battles. Due to this, enemies will spend the entirety of the battle using Stone on themselves and their teammates until all of them are defeated. The only difference between versions 1.0 and 1.1 is a bugfix for this.
Contributed by banshiryuu