Continuity mistake: The cake in this episode is first called "Upside Down Flint Rubble Bubble Cake." Later in the episode, it's suddenly called "Upside Down Flint Rubble DOUBLE Bubble Cake."
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.
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: When Fred and Barney are fighting over the television there are three knobs on the TV set, but when Wilma starts talking to Fred they have vanished, then they reappear.
Continuity mistake: While sitting down at the celebration dinner, Wilma has a blue dress and Betty has a white dress. When they get up and walk away from the table, they've swapped colours.
Continuity mistake: When Fred and Barney arrive at the Rockland Club, they park their car right in front of the front door. When Betty and Wilma arrive, they park their car in front of the door and Fred and Barney's car has disappeared.
Continuity mistake: At the 18th hole, Fred's opponent Ben Boulder hits his tee shot on the fairway. But we see Boulder doing his second shot, he doesn't hit the ball from the fairway; he hits the ball from the same tee box on which he did his first shot.
Continuity mistake: When Wilma is serving the two steaks for Fred at the dinner table, you can see there is steam coming out of the steaks, but when she places them in front of Fred the steam has disappeared.
Continuity mistake: When Fred and Barney arrive at the bowling alley, they are seen standing in the doorway, but the very next shot shows Fred inside the bowling alley and Barney is nowhere in sight.
Continuity mistake: Throughout the first season, Fred and Barney's boss' name changes from George Slate to George Granite and back.
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