Continuity mistake: At the end of the episode, Fluttershy reveals that she still has a fang left over from when she was a bat pony. This wasn't carried over, and her teeth have been normal since.
Other mistake: During Pinkie Pie's 'Smile Song', there is a scene where Pinkie Pie is jumping on a skipping rope (jump rope). Initially, the rope is held by two other ponies. However, at one point, these ponies are no longer holding the rope and the rope is just floating there. It isn't held by unicorn magic otherwise there would be a glow that appears when a unicorn holds something with magic, neither is anyone's horn glowing.
Baby Cakes - S2-E13
Other mistake: During Pinkie's Piggy Dance, she pokes out between the two babies. The female baby shifts over, then a lump appears on her chest that should be her front right leg. However, the lack of a line makes it appear to be on her chest.
Continuity mistake: In Pinkie Pie's Smile Song, at one point, there is a magenta pony with a purple mane. To her right are a yellow pony and a violet pony. To her left, there are a blue pony and a turquoise pony. In the next shot, the yellow pony and violet pony are on the wrong side of the magenta pony, separated by a mint green pony that was to the right of both the yellow and violet pony in the last shot. When the spinning shot plays, pay attention to the left of the screen to see the wrong order of ponies.
Continuity mistake: In the song, 'In Our Town', an earth pony spontaneously gets wings.
Factual error: Squirrels are seen woken from hibernation along with other animals, but squirrels don't hibernate.