The Fluttersleuth sequence is an homage to Problem Sleuth, the predecessor to Homestuck.
Rarity finds Sparkler's name appealing "for some undefinable reason", a reference to the G1 pony Sparkler who Rarity was based on.
A mysterious pony tries to remember Fluttershy's name — "Posie or something?" Again, a G1 reference.
The Batterqueen's retinue are all old-generation ponies. In her challenge against Minty, she makes a magic heart-patterned candy cane, while Minty presents a sock. This is a reference to the direct-to-DVD movie A Very Minty Christmas.
Non-pony mythology: For the baking competition, Love Lock hired an official time keeper. Said keeper is a curly-maned pony with a long scarf and hourglass cutiemark, aka the ponified Fourth Doctor, with the task of determining the best timed baker.
Most of the Rainbow Ponies are G1 characters who appeared in the "Ember's Dream" cassette story. As for Rainbow Dash's "Aunt" Ember, her design is based on this one's◊.
You cannot cross the fence because you don't know how to teleport.
If only you would encounter some sort of mother goddess figure of another species who could teach you to sort of shimmer in and out of existence, far more elegantly than even Twilight does. Such a shimmer would be wonderful.
One of Granny Smith's stories contains a Shout-Out to APPLE.MOV: "...and she ate eleven apples and five of those were in a single sitting! Why, the rest of us just sat there and stared, I can tell you. 'Apple Bloom,' we told her, 'you can't eat all those apples!' But she went and said..."
The shutting down of Ponibooru gets a nod when Pinkie explains how she had to abandon a certain hole she'd been using for her emergency stash of pony figurines. "Rest in peace, pony burrow."
Bubblecup says "I am not a clever pony", alluding to a certain fanmusician.
In order to enter the Medium, Pinkie Pie needs to destroy her cruxite artifact, shaped like Rainbow Dash, with a knife. Unlike a certain fanfic counterpart, she does not savor the idea of carving up Dashie.
The time-travelling Mysterious Mare-Do-Well paraphrases Back to the Future 2: "Third, if you ever have a daughter who, when she's eight years old, accidentally sets fire to the living room rug, go easy on her."
Pinkie Pie has a variation of shinigami eyes, as shown when she's setting up the Pegasus Rescue Party. In her case, it shows a pony's name, description and time until their next birthday, rather than time until death.