Continuity mistake: When Fez knocks the clown over and shatters it, you see the head roll in front of the body and out of frame with the nose still attached. Donna then turns around and runs in to take the nose from behind the body of the clown.
Other mistake: When Bob comes to order from the clown, he gets told to go away since they're closed. He starts pulling away, but you can see he doesn't leave the frame quickly. The edge of the car is still visible when the gang is sneaking back over.
Answer: It's Ashton Kutcher's dog.