Continuity mistake: Outside the windows of the house of Julia's friend it is daytime, but outside her front door it is night.
Continuity mistake: When we first see Eddie the radio announcer, his hair is blonde. But later on in the episode, his hair changes to a reddish colour.
Continuity mistake: When Fred and Barney are driving home in Fred's car, the hole in the back of the car changes shape between shots.
Continuity mistake: When Wilma and Betty are watching "Shinrock" on the TV, the camera cuts to Pebbles and Bamm-Bamm and the rug they are sitting on is covered with building blocks. Later on, when the two are trying to dance the "Pterodactyl", the rug is completely clear.
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