Factual error: Fez wears a Sergio Valente pullover, which is a company not founded until 1981. (00:02:20)
Continuity mistake: When Hyde enters the scene, his shirt is somewhat tucked behind his belt. In the following close-up shot his shirt is above the belt but returns to the tucked position in the next shot. (00:00:10)
Answer: It's Ashton Kutcher's dog.