Rainbow Dash claims that she can clear the sky in "ten seconds flat." Exactly 10 seconds elapse between Twilight's "prove it" response and the last cloud being kicked away.
At around 4:50 Nightmare Moon is seen in the hour glass when Twilight is passing it.
During the party scene, a grey pegasus pony with straw-colored hair is standing in the background. Initially her face is obscured, but after Twilight finishes pouring herself hot-sauce, the background pony's entire face is visible, and she's making an odd face with her nose scrunched and her eyes crossed. This pony was eventually popularized by fans and named Derpy Hooves.
At the beginning of the series, Twilight Sparkle is shown to live in an ivory-colored tower. This is an allusion to the phrase 'ivory tower', which means a world or atmosphere where intellectuals engage in pursuits that are disconnected from the practical concerns of everyday life. This is fitting for Twilight's character arc, as she starts out as an antisocial academic who needs to go out into the world and broaden her horizons.
Pinkie's prolonged gasp when she first sees Twilight is used again near the end when Rarity reveals Celestia is missing.