The Elements of Harmony (2) - S1-E2
Continuity mistake: When the ponies encounter the Manticore, it raises its paws and shows its undersides and Fluttershy notices something, even though nothing was there. Then when they stop attacking the Manticore, it shows its paw to Fluttershy to reveal a thorn, but the thorn wasn't there earlier. (00:05:25 - 00:06:20)
The Elements of Harmony (2) - S1-E2
Other mistake: At the end of the episode when Princess Celestia is talking to Twilight Sparkle you can see that Princess Celestia's tail is on top of her leg instead of in-between. It's covering her cutie mark.
The Elements of Harmony (2) - S1-E2
Other mistake: When Celestia is standing over Luna, her cutie mark looks elongated.
Factual error: Squirrels are seen woken from hibernation along with other animals, but squirrels don't hibernate.
Character mistake: When Rarity sees her cat stuck in the tree, Rainbow Dash is sitting next to the cat, but when you see her, her cutie mark is not there. (00:17:15)
Continuity mistake: Fluttershy's neck disappears after she says, "I don't know if I can cheer enough to help her".
Continuity mistake: When the characters reach the clouds and Rarity shows her wings, Applejack is wearing a helmet hat. But later on she has only a regular hat.
Deliberate mistake: When Fluttershy is telling off the cockatrice, her back legs and her wings turn to stone. But when she gives it the stare and the camera is right in her face her wings are outstretched.
Continuity mistake: When Rarity levitates the stick to mark a spot where she detected the gems, she drops the stick right after a guard "threatens" her. Then, in the same scene, the stick has mysteriously disappeared.