As part of the quest to gain the Harvest Dance emote, you must speak with a young boy who, among his musings, says, "Ummm...scoop with both hands, then look left, up, up, right, down... Or is it up, up, down, down, left, right, left, right? I wish she would let me take notes..."
In 3.2's Hildibrand quests, the dialogue box before accepting the first quest notes that "You cannot help but wonder if you are about to have a bad time." Later, when invited to wait in the gazebo outside of Fortemps Manor, Nashu panics at the prospect of being attacked by the gazebo. The poor guard talking with you two, plays the role of the exasperated Game Master
House Fortemps Guard: "It's...it's a sodding gazebo..."
In the level 60 quest for Bard, Guydelot has his own criticism for the Final Boss.
In the Coerthas Western Highlands, the local multi-man boss FATE is called "We Fought a Dzu".
In Idyllshire, is the FATE Olmpus Has Pollen. The enemy being Plant creatures, whose pollen has overwhelmed the goblins gas masks and is causing them to have runny noses and causing their eyes to tear up.
In Azys Lla, there is a FATE called Harvest Moon. Said FATE pits you against Clockwork Harvestmen (mobs based on XII's Mimics)
A FATE involving protecting honeybees is titled "Now I See Bees I Won", which is a lyric from the song "Bob" by "Weird Al" Yankovic
Mob and NPC Names
The Warrior Job quests are all given to you by a Roegadyn named Curious Gorge.
The leader of the millers in the "Poor Maid's" FATE chain in La Noscea is named Rabid Ratata.
One of the Elite Marks in Western La Noscea is a crab named Dark Helmet.
The first boss of the Keeper Of The Lake is named Einhänder. And if you know the game that references, then you'll have a good idea of his main gimmick - namely, that he will switch out weapons that he carries underneath, from a bar to a minigun to a cannon. Later on, during the final boss fight of Keeper of the Lake, and much latter on, in Heavensward in the Sea of Clouds region, you'll find the same style of enemy mobs that appear named "Astrea" and "Endymion". Both are the name of the actual ships players controlled in Einhänder.
Within the Antitower, there is a Spriggan boss called "Ziggy", accompanied by a number of adds it spawns called "Stardust". This is especially notable because this boss came out in patch 3.2, the first since Bowie's passing.
Mentioned below, the recurring bosses of the Midas portion of Alexander have slightly altered versions of the names of the Combaticons. Onslaught-Onslaughter, Brawl-Brawler, Vortex-Vortexer, Swindle-Swindler, Blast Off-Blaster and finally Bruticus-Brute Justice.
One of the potential NPC racers in the Chocobo Race is Legally Yellow.
2016's Moonfire Faire centers around a Sentai trio called the Posing Rangers. The name of the team, premise and explosions may bring Super Sentai or Power Rangers to mind.
The boss of Alexander: The Heart of the Creator, the Ark summon from IX, was renamed Cruise Chaser, and has the designation "Blassty." This is a shout-out to the 1986 game Cruise Chaser Blassty which the Ark summon was originally a reference to in the first place.
Similar to the FATE above, you can recruit a Hellsguard named "Careless Whisper" to your adventurer squadron.
Quest and Guildleve Titles
A mission that you need to take to obtain a permit to get a Chocobo mount is called My Little Chocobo.
A few quests later and you are sent by the Order of the Twin Adder to find the Sylph elder in a quest called Spirited Away.
There is a quest called Wretched Hive of Villainy. The questgiver opens by saying the location (a "hive" of the bandits known as the Redbelly Wasps) wasn't always a "wretched nest of scum and villainy".
There's even a shout out to This Very Wiki! One of the quests is called "Enemy Mine" and it involves someone in the South Shroud asking the Coeurlclaw Poachers and Redbelly Wasps to look out for Garleans.
The quest to unlock Hard Mode for Tam-Tara Deepcroft is called Corpse Groom.
One main scenario quest during the lead-up to the initial Titan trial is titled There and Back Again. Interestingly, it's given to you in Southern Thanalan, one of two zones in the game where you can find firedrakes, which is what Smaug is sometimes classified as.
One guildleve quest in Coerthas is called "We Can Dismember It For You Wholesale", a reference to a Philip K. Dick short story titled "We Can Remember It For You Wholesale", which in turn was the basis for the movie Total Recall (1990).
There is a quest in Ul'dah is entitled "Tougher than Leather", the name of two albums by Run-D.M.C. and Willie Nelson, as well as lyrics from the song "Unknown from M.E." from Sonic Adventure.
Of course, there's always the quest given in Coerthas called Dead is Dead.
A levequest that seems to reference This Very Wiki is dubbed "Tropes of the Trade".
One of the sidequests in the Dravanian Forelands has you accompanying a new hunter on her first hunt. The quest's name? I Wanna Be The Hunter. (Just be glad you don't have to deal with any upwards-falling fruit!)
the Quest to unlock The Great Gubal Library (Hard) is "Let Me Gubal That For You", and the end of that quest revealed that the point of revisiting the dungeon is to claim the index of the library's contents.
One vanity pet you can own is a gray cube with legs and wings called the "Demon Brick". It is believed to be a shout-out to World of Warcraft developer Ghostcrawler, who famously expressed his annoyance with theorycrafters by saying they'd use a featureless gray cube for a pet if it gave them a little extra DPS.
This has been debunked - the Art of Eorzea artbook explains that it is actually meant to be a minionized version of the Demon Wall boss.
One of the attacks used in the final fight for Tam-tara Deepcroft Hard Mode is Red Wedding.
The final boss of Hullbreaker Isle is a Kraken, who uses an attack called At World's End.
Continues on into Sastasha (Hard), where the Kraken is summoned by a pirate (who thanks to a mutation resembles Davy Jones) shouting "Release the Kraken!" and a new attack from the Kraken being called "On Stranger Tides"
The scene in the main scenario where Nabriales stops Moenbryda's axe effortlessly and with a single finger is very reminiscent of Aizen's reveal as Big Bad in Bleach
Godbert Manderville in the course of the 'Her Last Vow quest line reveals is own version of the melee Limit Break 2 Bladedance, with a Giant Golden Hammer that engulfs the enemies in a golden light.
The 2015 Little Ladies' Day event includes an item called "Nanapasi's Happy Smile Super Wish Bag". The description indicates that he wanted to call it the "Happy Smile Super Challenge Family Wish Bag", but the name wouldn't fit neatly into a single line.
A golden saucer quest is called "So You Think You Can Ride This Chocobo", could be a reference to So You Think You Can Dance.
The Monk's One Ilm Punch is an Eorzean flavored shout out to Bruce Lee 's famous One Inch Punch, complete with Bruce Lee-esque posturing afterward.
The Twintania mount has an "attack" (does no damage since every mount with an attack ability is just for show) called Aerial Combat Maneuvers and its info box simply says "Do a barrel roll!" Twintania even does said barrel roll when you command her to do it.
The Dark Knight's Living Dead buff will protect the player from being knocked out and they gain a zombie like debuff should they suffer a blow that would have put them down. The debuff is called Walking Dead.
The Dusk Vigil dungeon contains a number of references to the Night Watch from A Song of Ice and Fire. The dungeon is a huge ice-crusted wall of a fortress in the frozen north, similar to the Wall. The dungeon's name, "Dusk Vigil" means the same thing as "Night Watch". The dungeon is filled with undead, icy zombies of the former defenders, similar to the Others the Night Watch are meant to defend the realm from. The quest to unlock the Dusk Vigil is titled "For All The Nights To Come", which is the last line of the Night Watch's oath. In addition to that, the last boss of the Dusk Vigil has an attack named "Winds Of Winter".
The final level 60 quest for Culinarian ends up with a pure tribute to a Shokugeki in Shokugeki no Soma.