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: During the hearing, when Perry Masonry is questioning his client about being fixed financially, part of Perry's string loop closure on his clothing vanishes within the same shot, and then reappears. A few moments later Perry's two parallel strings are crisscrossed, then both are back to normal. Later, when Barney asks Perry if he can hold Bamm-Bamm, once again Perry's parallel strings become crisscrossed. (00:20:35)
Continuity mistake: When Barney and Betty are at Child Welfare Authority, Bamm-Bamm is sitting on the counselor's desk right beside her, but in the shot facing Betty and Barney, the baby boy has vanished. (00:15:00)
Continuity mistake: When Betty and Barney are at Child Welfare trying to adopt Bamm-Bamm, the black strap over Bamm-Bamm's shoulder switches from his right shoulder, to his left, then back to his right. (00:14:45)
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