Expy: Rainbow Dash for Sonic the Hedgehog. She's derived from multiple versions of the character: she shares a voice actor with the Sonic F incarnation, classic Sonic sound effects play when she does just about anything, and she even quotes the theme song from Sonic Sat AM as it plays. No surprise her element is that of The Homage.
This also makes her Equestria's equivalent to Jesus, according to The Doctor.
Freeze Frame Bonus: For a less-than-a-second moment around 2:48 in episode 3, right after Applejack's comment regarding Capcom and Apple Bloom's aggressive marketing, this comment flashes on the screen:
The views and opinions expressed herein do not necessarily reflect those of Camaraderie is Supernatural cast and crew. However, we eagerly anticipate the longest day of the thousandth year, in which the stars shall aid in Mega Man Volnutt's escape from his orbiting lunar prison.
Genre Savvy: Fluttershy, apparently. After the battle with the manticore:
Twilight Sparkle: Wait, what did you do? Fluttershy: Thorn in his paw; it pays to know your classic Aesop from time to time.
Twilight Sparkle: What do you take me for, an idiot?! Applejack: As tempting as it is to give the obvious answer, I need you to trust me.
Screw Destiny: The entire point of the Cutie Mark Correcters in Episode 3.
Self-Deprecation: In the Audio Commentary for episode 1, Mystic Pyro Freak openly admitted that she came up with the idea of Applejack slipping accents to make fun of the fact that she couldn't keep a consistent one.
Pinkie saying she's in "a crappy parody series done by a talent-less hack."
Nightmare Moon's intro has her ridicule the idea of a parody series as legitimate comedy.
Since when does such nonsensical, unfunny tripe qualify as comedy?
Music from Tengen Toppa Gurren Lagann plays when Twilight figures out how to activate the Elements of Parody, their activation is accompanied by the power-up sound effects from Dragon Ball Z, and the main characters proceed to blast Nightmare Moon with a "Giga Parody Breaker".
Stealth Pun: After the RPG battle in episode 2, Rainbow Dash levels up and gets +19 coolness, which prompts her to complain "Aw, crap! Just short!" Assuming she had 100 coolness before, one more point would have made her 20% cooler.
Straight Man: Fluttershy's role in the series, given that this is the Element of Parody she embodies.
Part of Apple Bloom's "eighties training montage" in episode 3 involves a nod to Punch-Out!!.
Suspiciously Specific Denial: Celestia's letter to Twilight in the first episode includes the claim that her being sent to Ponyville "totally isn't a thinly-veiled Batman Gambit meant to prevent the impending pony apocalypse. For serious."