Continuity mistake: When the penguins disguise themselves as a snowman, the nose of the snowman is a penguins beak. After they bump into the elevator, there is a carrot lying in the pile of snow. But the carrot was never part of the disguise.
Continuity mistake: When Private escapes while the other penguins aren't looking, he doesn't put a bowling pin in his bed to trick the other penguins into thinking he is still there. A few shots later when morning arises, there is a bowling pin in his bed.