Continuity mistake: Wilma opens the bedroom door to find Fred covered in flour, but in the next shot the bedroom door has vanished while Fred stands in the doorway.
Continuity mistake: When Fred has a nightmare he drops his pillow on the floor, and just as Wilma gets out of bed to pick it up, Wilma's pillow simply vanishes into thin air within the same shot. (00:13:50)
Continuity mistake: While Fred and Barney are fighting, when Pebbles and Bamm-Bamm are devising a plan together in baby-talk, the black strap is over Bamm-Bamm's left shoulder, but when Bamm-Bamm walks past Fred and Barney the strap is over Bamm-Bamm's right shoulder. (00:22:55)
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: While Fred is giving Roger a few baseball pointers, Roger's wearing something that only goes over his right shoulder, but then it switches to going over his left shoulder when Fred "teaches" Roger to slide. (00:05:45)
Continuity mistake: While Fred and Barney are being chased by the police, in the closeup of the stop/go signal we see two ropes beside the monkey's hand - one controlling "stop" and one for "go", but in the wideshot there's only one rope hanging from the post, apparently controlling both "stop" and "go" signals. (00:19:55)
Continuity mistake: When the two couples sit down on the couch to watch Peek-a-Boo Camera on TV, there's an antenna atop the TV in the wideshot, but the antenna has vanished in the TV's closeup.
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)
The Monster from the Tar Pits - S1-E7
Continuity mistake: When Fred comes in wearing the monster costume, there's a handle on the interior side of the door, but it vanishes when Fred hides to scare Barney.
Continuity mistake: During the circus performance, Rodney the knife thrower is wearing a one-shoulder outfit, which repeatedly switches from his left, to his right shoulder, and back again. (00:17:30)
Continuity mistake: After Fred and Barney leave for the hospital without Wilma they realise the mistake and head back to the house, and when it cuts to Wilma in the bedroom Dino jumps atop the blue blanket on the bed, but in the next shot the blue blanket is gone, and then it reappears for Dino to hide under. (00:16:35)
Continuity mistake: When Sandy puts the cigar into Fred's mouth, he lights the cigar and it explodes, leaving Fred's face covered in black marks. In the next shot, the marks have disappeared.
Continuity mistake: When Fred, Wilma, Barney and Betty arrive at the Ferris Wheel, there is a queue of people behind them. When the circus owner listens in on Fred and Barney's conversation, the queue has disappeared.
Continuity mistake: During Fred's dream sequence, Fred tells Barney that he missed watching Pebbles and Bamm-Bamm grow up and behind Barney there is a table and a painting on the wall. In a close-up of Barney in the next shot, both the table and painting have disappeared.
Continuity mistake: When Wilma is trying to help Betty find a part-time job in the newspaper, you can see that there is a light blue cloth at the end of the line, but when we see Pebbles playing with Dino in the next shot, the blue cloth has disappeared.
Daddy's Little Beauty - S4-E12
Continuity mistake: When Fred is trying to work out what kind of talent Pebbles has, she has her bathing suit on. When Pebbles is seen crawling onto the stage when it's her turn, she has her regular clothes on, and when Pebbles is on the stage with Dino, she has her bathing suit on again.
Continuity mistake: When Detective Shale knocks at Fred's door, he is wearing a blue suit, but when he enters the door, his suit is now yellow.
Continuity mistake: The "8" on the side of Fred's car keeps changing style throughout the race sequence.
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