Monster Fred - S5-E2
Continuity mistake: When the doctor puts Fred into the trick box you can see that the box is quite small, but after a quick cut to Barney we return to the doctor and the box is much longer.
Monster Fred - S5-E2
Continuity mistake: In the dinner scene towards the end of the episode, the dish in front of Fred has very little Chinese food in it, but when Pebbles wants some, we cut back to Fred and more has appeared.
Monster Fred - S5-E2
Continuity mistake: When Barney is driving Fred to the doctor after his accident at the bowling centre, you can see that Dino is sitting behind him in his car, but in the shot where Fred says "I don't want to see a doctor!", Dino has disappeared.
Monster Fred - S5-E2
Continuity mistake: When Fred is holding his bowling ball in Alley 13 at the bowling centre, you can see there is a bowling ball rack behind him, but in the next shot the rack has disappeared.
Monster Fred - S5-E2
Continuity mistake: After Fred brakes his car to avoid hitting the black "Catosaurus", Barney's hands can be seen on the front of the car, but they're not on the car in the next shot.
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