Continuity mistake: When Fred and Barney are driving their car through the One-Way tunnel, the edge around the hole at the back of their car is smooth, but when Barney turns right to go through a tunnel, the edge is now torn.
Continuity mistake: When Fred and Barney discover that the football match on TV has been postponed, we see an interviewer sitting at the desk and you can see there is a nameplate saying "T.V." in front of him, but when the interviewer introduces Eppy Brianstone in the next shot, the nameplate has disappeared.
Continuity mistake: When Fred carries a plate of sandwiches to watch the football on TV, the TV channel knob has nothing around it, but when Fred switches on the TV to watch the football, there are now dots around the knob.
Continuity mistake: When we first see the Flintstones' house at the beginning of the episode, the handle is on the left-hand side of the door, but when Dino walks out of the house after Fred tells him to play outside, the handle is now on the right-hand side.
Continuity mistake: When Fred is performing "Let The Sunshine In" at the end of the episode, you can see that his right foot is next to Bamm-Bamm on the rug, but in a close-up of Pebbles and Bamm-Bamm, his foot has disappeared.
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