"Oh! Did you find a new friend?" *crushes apple* "I killed it!"
The running gag where Twilight keeps running past Bon Bon, who is watering flowers.
Twilight: You know what? I'm not even mad at you. You stick to your principles.
Read It and Sleep
Twilight apparently being an avid fanfic writer who ships "Applesack" and "Charity" together. When Applejack and Rarity have to stay at Twilight's house, she forces them to re-enact all 70 chapters of her story.
At the end of the episode, Twilight sends her fanfic to Princess Celestia, who has a great reaction to Twilight's letter telling her about it.
Princess Celestia:Please let it be a one-shot!
Twilight: Enclosed are all seventy chapters!
Celestia: (getting swamped in chapters) GUAGH!!!
Dragone Baby Gone
Applejack: With just a little teamwork, we can all-
Twilight: I'm going in alone!
Every time Applejack or Rainbow Dash's elements are brought up, the words "loyalty" and "honesty" are clumsily overdubbed with one another, a gag on the common fan perception that each would have been better suited to the other's element. Making it even better is the fact that the dialogue is structured so that the other word would have clearly fit better.
Applejack: I'm the element of [HONESTY], and I think the loyal thing to do is stick together!
Rainbow Dash: As the element of [LOYALTY], I can honestly say that this ball is awesome!
Cute from the Hip
The lecture on robots.
If you put the vid on captioning, you can read about Cheerilee thinking her husband was a robot.
The Equestrian national anthem.
As if Bon Bon's "I didn't put those in my bag!" line wasn't funny enough by default in the original, it gains an even more Jerk Ass tone...
Many of Diamond Tiara and Silver Spoon's lines in "Cute From The Hip" combined with their male voices:
Diamond Tiara: Hey, Cakey is MY best friend, I get to decide when she dies!
Twilight: Also, now that I have everything I could ever want, how do I know if I'm happy?
Spike: This calls for a hug!
Twilight: Now that I've fulfilled all teenage pony fantasies, what more is there for me to take by force?
Spike: You don't need anything else, Twi! You just need someone to pamper you until you die!
Celestia explaining to Twilight about why she must go on her mission:
Celestia: Twilight Sparkle, I have just been informed that we are in the midst of a very delicate political crisis. I gave you the very simple task of greeting the centaur ambassadors, and you put on an entire five hour puppet show centered around racist characters of their culture and religion!
Spike: And, she stole their crown!
Celestia: You've got to be kidding me. I think the best course of action would be to find some kind of nonsense task and send you away for a while will we fix things.
Twilight: My own special mission? Will I learn about magic? And friendship?
Celestia: Oh yeah, yeah, sure, friendship and magic, more of that stuff...
Luna becoming more unintelligible than ever while giving Twilight her instructions, which Twilight claims to understand perfectly. And this includes saying hi to herself in the mirror.
Luna: Oh hi, Luna. This portal has been safely hidden away for centuries...in our bathroom. Your mission on this adventure is to re-establish many bases of contact about different global fighting, spiral into numerous times and making stampy noises backwards of into and from within different complex alfalfa mainframe and eventually to save the world.
Their take on the infamous "moons" issue is that it has nothing to do with the actual moon and is just the pony way of saying "38 seconds."
Celestia: Hurry, or we'll have to wait another eight minutes!
Twilight's actress explaining that there are other people in the house, so she can't scream properly.
The Take That song to the movie's whole concept, making a film adaptation with a setting so much more dull and pedestrian than what's typically in the show.
Which then cuts to a random onlooker, revealing that Twilight's just singing and dancing to herself.