Continuity mistake: When Fred is telling Barney, Betty and Wilma about his adventures, Betty can be seen sitting next to Wilma at the table, but in the next shot Betty has suddenly disappeared.
Continuity mistake: When Sheriff Craig is performing the ropes act, Fred can be seen sitting next to Barney at the table, but in the very next shot Fred has disappeared.
Continuity mistake: When we first see Betty and Wilma in the caravan, the outside view shows two windows and it seems they are sitting well apart from each other. But inside the caravan, they are sitting much closer to one another.
Continuity mistake: When we see Fred and Barney in the car, Barney produces a geiger counter. In the close-up, he pushes a button and the flap opens to produce a cricket inside the machine, but in the very next shot the flap has suddenly closed.
Continuity mistake: When Wilma is scrubbing the deck on Columbus' boat, you can see she has Betty working beside her, but after Barney asks "A mutiny?" we cut back to Wilma and Betty has vanished.
Continuity mistake: During the jousting scene, the King and Queen keep changing positions from standing up to sitting down on their thrones between shots.
Continuity mistake: When Fred wins the jousting competition, the King tells him that he has won his daughter, Princess Lenor, but in the next shot when Fred asks, "What do you mean, I've won her?" Lenor has suddenly disappeared.
Continuity mistake: When we see the dial on the Time Machine, it initially has six segments, but when we see a close up of the Time Machine inventor putting his hand on the dial, it has now has seven segments.
Continuity mistake: When Fred and Barney rush off to have a go on the shooting gallery, Wilma's eyebrows disappear but then re-appear when Betty says "Aren't they cute?".
Continuity mistake: When we see Wilma speaking in Fred's car at the start of the episode, the hole behind her changes from small to large between shots.
Superstone - S5-E24
Continuity mistake: When Fred is sitting at the dinner table with Wilma and the Rubbles, you can see he has a knife in front of his hand, but in the next shot the knife has disappeared.
Superstone - S5-E24
Continuity mistake: When the producers tell George to put his Superstone costume on, you can see one of his bags is next to his dressing room table, but in the next close-up of George, the bag has disappeared.
Continuity mistake: When Fred is at Barney's house, he knocks on the door and says, "Open up, Barney, it's me!" When the door opens, Fred's arm disappears.
Superstone - S5-E24
Continuity mistake: When Fred and Barney are in the bar, the barman asks them "What'll it be, you guys?" and you can see there is nothing on the counter, but in the very next shot a bottle has suddenly appeared.
Superstone - S5-E24
Continuity mistake: When Fred and Barney and the gang are watching "Superstone" on the TV, the TV has an aerial on top of it, but when we see a full view of the TV, the aerial has disappeared.
Superstone - S5-E24
Continuity mistake: During the bank robbery in "Superstone" on TV at the beginning of the episode, the amount of money in the robbers' bag goes from empty to full between shots.
Superstone - S5-E24
Continuity mistake: When Fred (as Superstone) is putting the powder on his face in his dressing room, he puts the powder puff back in its dish, but when the door knocks, we cut back to Fred, and the powder puff has disappeared.
Continuity mistake: When the poker players hide under the table, you can see there are blue chips, white chips and red chips on the table, but when Sheriff Craig leaves, the blue and white chips have changed places and the red chips have disappeared.
Continuity mistake: When the man gives Sheriff Craig back his badge, his moustache disappears when Craig is talking to him, but comes back when Craig runs away to pick up his bags.
Continuity mistake: When Sheriff Craig is hiding under the table, he says "But I'm not that sheriff" and you can see part of his feet outside the table. In the next shot, Craig is now completely under the table.
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