Other mistake: During the closing theme (early seasons), when Fred walks by to close the birdcage, Wilma is shown in the background sleeping and her entire mouth is missing.
Continuity mistake: In one episode, an old friend of Wilma's calls Wilma "Wilma Pebble" (using her maiden name, unaware she got married). Later in the series, as well as the 1994 movie, Wilma's maiden name is revealed to be "Slaghoople."
Answer: The name of the pet is "Baby Puss." He has appeared in episodes, but only a very few. The first episode was probably "The X-Ray Story" from season 2.
Bishop73