Continuity mistake: During the adoption hearing, when Perry Masonry rebukes Barney about his "failing memory", Perry's string loop closures on his clothing suddenly vanishes mid-shot, then they reappear. (00:21:50)
Continuity mistake: When Barney, Betty, Wilma, Bamm-Bamm and Pebbles are on the bridge at the end of the episode, Bamm-Bamm's white hair turns red like Pebbles', then changes back to white when they all start laughing.
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