Other mistake: During the closing theme (early seasons), when Fred walks by to close the birdcage, Wilma is shown in the background sleeping and her entire mouth is missing.
Other mistake: At the start of the episode we're shown a preview of the episode's plot: while Fred stretches his leg on the ballet bar his leg gets stuck and when the ballet teacher pushes his leg down, the part of the ballet bar which Fred is leaning on is gone. What's odd is that during this scene within the episode the ballet bar is perfectly intact. (00:00:25 - 00:14:40)
Other mistake: When the shopkeeper takes the magazine away from Fred in the supermarket, Fred says he was just looking at the pictures. But when the shopkeeper takes the magazine, you can see that the page Fred was reading is completely blank.
Other mistake: When the Inventor asks the Flintstones and the Rubbles if they are game enough to try his Time Machine, Betty says, "Golly, I don't know." After Betty says the line, her nose disappears.
Other mistake: In the "Old MacDonald" sequence, Fred tells the scouts that whoever he points to will sing the chorus in their own language, yet the German and Dutch scouts sing it in English.
Other mistake: When Fred puts his hand on the knob to turn on the television to watch the football, he turns the knob clockwise but when he takes his hand off it, the knob has not moved at all.
Other mistake: Fred's telephone cord is missing when he and Loudrock are calling their friends about the puppies.
Monster Fred - S5-E2
Other mistake: Fred's mouth doesn't open when he says "Now knock it off!" to Barney in his car.
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