The Cameo: Gogo the Mimic, one of the secret characters, is replaced by Lauren Faust as an alicorn. Many other cameos show up as well, such as Sethisto as Cid, Daniel Ingram as the Impresario, Snips and Snails as Biggs and Wedge, and Daring Do as Siegfried.
Carrying the Antidote: Discord drops a Harmony Band after your first battle with him, an item which blocks two of the statuses he frequently inflicted during the battle. That would have been really useful beforehand... then again, I guess this kind of behavior makes perfect sense coming from Discord.
Character Name Limits: The game only lets you input up to six letters in a name, while most of the characters have names that are longer. To get around this, most of them have nicknames, such as Twilight = Twi, Applebloom = Bloom, Celestia = Tia and so on. Their full names still appear in certain cutscenes. Early versions included a tag to 'Please keep the name'; later revisions simply ask you to 'Enter Pony Nickname'.
Composite Character: Arguably everyone, but special attention should go to Commander Derpy "Hurricane" Hooves.
Crapsack World: It may be with ponies, but everyone who dies in FFVIwill die here, and those who can die depending on your choices (Fluttershy if you leave the Floating Continent too early, Sethisto if you don't catch enough yummy fish) aren't exempt either.
Disc One Nuke: Pinkie Pie. Some of the Random abilities she can pick up right after you find her (assuming you've encountered the right enemies) are really powerful, including level 2 spells when your unicorns have only level 1, and the dreaded "Cat Scratch", which can do four-digit damage when your heavy-hitters do three. Even better, she ignores Gau's original flaw of becoming uncontrollable after you've used the ability, so she's flexible too.
The Dreaded: Fluttershy, thanks to rumors about The Stare.
Early-Bird Cameo: Overlapping with A Taste of Power in a weird way. You don't get properly introduced to Espers and how they work until Las Pegasus, but unlike in the original game, you actually get your first Esper earlier, just after getting Celestia. (Presumably because she stands in for Edgar, whose Tools were given to Applebloom, so they had to find some other gimmick to have her show us. They also needed to explain that, unlike in the original, only Unicorn characters can equip Espers in this game.) This has another strange side effect: the game doesn't start telling you you're getting Magic Points from battles (or explain what they are) until you're 'supposed' to, but if you've been using Unicorn you'll have been already getting them for most of the game.
Leads to a bit of a Plot Hole when you get to the Magitek Facility and see Unicorn imprisoned there despite already having it.
Easy Levels, Hard Bosses: BIG TIME.Word of God says this is intentional. Most regular enemies give little trouble, and the way skills are redistributed leads to a few Disk One Nukes. The bosses on the other hand, are another story, especially seeing as Espers no longer give stat boosts. Even tutorial bosses can and will kill you if you're unprepared.
You know those eight elemental dragons that were easy to counter with the right equipment? Well, their magic isn't blocked by such barriers anymore. That's also not to mention the fact that they deal tons of damage for each physical attack as well. Oh, and did we mention they revive with full health after you'e killed it once?
The Demon Train. With two party members that can preform a suplex on it, you'll be tempted to do so. It now counter attacks when hit with with that specific attack.
Epic Fail: Invoked; the 'Miss' graphic for when someone doesn't hit a target now reads 'Fail'.
Even The Mares Want Her: Given that Applejack has taken Cyan's role, there's a bar floozy who hits on her, much to AJ's consternation.
Applejack: Now see here, missy, mah barn door don't swing that way!
Furry Confusion: A Unicorn Esper being summoned by Unicorn player characters, anyone? Made stranger by the fact that only Unicorns (and Alicorns like Celestia) can equip Espers.
There's also the oddity of seeing bipedal ponies riding chocobos.
Gameplay and Story Segregation: You see Rarity using several Ice spells while attempting to put out a house fire in a cutscene. When she joins your party a few minutes later... she doesn't know any. (She does know a Water/Wind based Blue Magic attack, but it would have been a bit weird to hear her yell out "Aqua Rake" in said scene)
Hyperactive Metabolism: Healing items are replaced by strains of apples, and MP recovery items with flavors of soda-pop.
Jack of All Stats: Celestia, at least early on. Decent physical attack, can use some Magic (but not as well as Twilight) while NOT being a Squishy Wizard. Which makes sense, seeing as she has the power of all three pony races. Once stronger physical fighters like Luna and Applejack join though, she's better used as a pure mage. (Still less squishy than Twi and Trixie though)
Konami Code: Used as the input code for Luna's Reiki skill.
Least Rhymable Word: Zecora's last words set up something to rhyme with "orange." Naturally, Discord kills her before she would have finished the verse.
Magic Knight: It's possible to make Luna one if you teach her magic from Espers. Celestia is one to begin with.
The Magic Went Away: Due to the War of Chaos, magic was almost completely lost 1,000 years ago. This led to unicorns falling into obscurity, as the ability to cast spells became a rarity. Even Celestia and Luna were affected, though they didn't lose their immortality.
After kidnapping Trixie and finding out she's not Maria, Rainbow Dash tersely asks if she's a spy.
A few of Discord's lines from the show are quoted verbatim in somewhat similar circumstances. Most notably his cry of "Arreviderci!" when he kicks a mortally wounded Emperor Gilda off of the Floating Continent.
During the escape from Discord's Tower, Rainbow Dash remarks that she's becoming more and more like Firefly every day. As CR once noted, Rainbow Dash is an Expy of Firefly.
The Impresario is (usually) renamed "Ingram" after Daniel Ingram, the series' song writer.
There is also an NPC in Stalliongrad who asks "Who is funnier? Mike or Joel?" Picking "Joel" summons guards to fight.
There are also at least two Skyrim references. Naturally at least ONE GUARD will talk of being retired due to an arrow in the knee, and there is an enemy in the game who can blow an ally with Fus-Ro-Dah.
Both Luna and Applejack have had moves renamed from the original FFVI moveset to refer to other games. Sabin's Blitz is now Hadouken, while Cyan's Tiger/Slash is now Ryuenjin.
When arriving in the Esper World in a flashback, Emperor Gilda gives this command.
When Applebloom gives a vague answer to Trixie's question about why she saved her in South Canterlot, Trixie remarks that Applebloom must have some "Past Sins" to atone for.
Some of the sprites were made by MasterRottweiler which were based on characters from Diablo 2.
Commander Hurricane (Derpy to her friends) mentions that even after all that has happened, Equestria will prevail. Her portrait was drawn by Equestria-Prevails.
On the Phantom Train, when Daring Do shows up to keep you from taking the treasure near the front of the train, Luna tells her "We are not amused!"
Spared by the Adaptation: Despite playing the part of Shadow, Fluttershy's attempted suicide is interrupted by Rainbow Dash in the ending. She's still nowhere to be seen on the deck of the airship though.