Factual error: In the final surfing scene, Cody and Z are surfing, presumably, off into the sunset. However, being on the north shore (given Z's remark a few moments before), that would mean the wave is rolling to the south which would put the sun toward the east not the west. (01:20:00)
Audio problem: At the scene where Mikey asks the elder penguin if anyone surfs in Shiverpool, when he says,"You know you're standing on thin ice," his beak never moves.
Continuity mistake: Right before the final race, there is a wide shot of all the surfers. In that shot, Cody has his Big Z necklace that he chucked earlier.
Answer: There is a UFO in the "Z is for Zurfing" scene and one where it shows Chicken Joe's dad, Chicken Bob in the background of the bucket.