Continuity mistake: When Fred goes over to Wilma after she drops the cups and saucers after seeing him shrunk, the broken crockery that surrounds him is completely different to what's seen in the previous shot.
Continuity mistake: In the scene where Fred and Barney are in the doctor's surgery, the doctor produces a lollipop for Fred. When he produces the lollipop, you can see it's well away from Fred, but as the shot changes the lollipop is much closer to him than it was in the previous shot.
Continuity mistake: When Fred tells Wilma that he is giving up inventing for good at the end of the episode, you can see that Betty is sitting next to Wilma on the couch. When we see a close-up of Fred in the next shot, Betty is missing.
Dr. Sinister - S5-E8
Continuity mistake: When the aeroplane arrives at Dr Sinister's volcano, Fred and Barney are led down the stairs by the three crooks, but when they arrive at the sliding door, one of the crooks has gone.
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