The giant worm that Twilight and Cadance battle is called a "Tatzlwurm" by Meghan McCarthy.
Near the end of Discord's song number, Discord is seen posing with a glass of water with Twilight and Cadance behind him, mimicking the poster of Star Wars: Episode IV - A New Hope (1977).
The finale of Discord's song has him sit in a chair and pull a rope to get himself soaked, like Flashdance (1983).
Friendship Report: Twilight learned even the most chaotic of days can be a great experience, even with her friends.