While Baby Mumble is with the Skuas, a small black bow can be seen on Mumble's chest. However, when Mumble falls into the crack in the ice, the bow disappears. When the birds fly away, Mumble rolls to the side and begins to cry, with his bow visible again.
When Mumble and the Amigos are outrunning the avalanche, Mumble hangs in mid-air for a few seconds, and Ramon grabs onto Mumble from behind before they fall. Looked at closely, Ramon's flipper passes through Mumble's feathers right before they nose-dive down the slope.
The goof items below may give away important plot points.
Errors in geography
On a zoom out sequence to the globe, the Aquarium where Mumble is held is revealed to be in Miami. That Aquarium and the surrounding park do not exist however. Additionally, the aerial imagery in the movie is flipped.
When Mumble is in the aquarium, there is a long zoom out until the earth is visible as a small disk in space. Stars in the background twinkle. However, stars should not twinkle when seen from space. They only twinkle when seen from earth because of variations of the atmosphere.
Toward the end of the movie, the penguins start to dance while a human video tapes them. Later, the video of the penguins dancing is played in Times Square and on TVs all over, but the human didn't even have his camera out yet during the beginning part of the dance that is televised.