Other mistake: During the climax, when Junior reactivates the baby manufacturing machine, the first baby to emerge from the machine is naked. The machine's hands diaper this baby. However, when the other babies emerge from the machine they're already wearing diapers. (01:15:45 - 01:16:25)
Other mistake: When the Stork is hit with a stick, "Perfect!" is heard in his voice. However, the stork had been knocked out when it is heard and we aren't shown who shouted "Perfect!"
Chosen answer: Hunter had allowed the penguins to take care of the baby, and will then be returned to the human world when she is an adult. The penguins were taking the baby back to their home to raise it.
Casual Person