Continuity mistake: When we see a close-up of Fred's car during the race, you can see there are two cars in front of him and there is nothing behind him, yet in the next shot he is being passed by a purple car.
Continuity mistake: When we first see Fred's car at the Indianrockolis 500, the car has nothing on the side of it, but when we see the car at the start of the race, a number "8" has suddenly appeared.
Continuity mistake: When Wilma is shocked to see Fred on the television, you can see behind her there is a window and curtains, but when we see Wilma in the next shot, the window has disappeared.
Continuity mistake: When we see Fred and Barney singing "Doo Dah" in the car while on their way to the track, Barney is sitting in a single seat, yet a close-up shot shows him sitting on a longer seat.
Continuity mistake: When we see Fred and Barney in the car on their way to the track, Fred's front seat is missing.
Continuity mistake: When Fred goes past Wilma into the living room to watch TV, he has a fish sandwich and is carrying a tray with a drink and a bowl of snacks on it. When he is watching TV, the bowl of snacks is nowhere to be seen.
Continuity mistake: When Fred drops the tyre on his foot, he hops around in pain and you can see that Barney is holding the tail on the turtle. When Fred says, "Now you tell me!" we cut back to Barney, and the turtle has gone.
Continuity mistake: Fred is on a ladder lighting a candle - the top legs of the ladder are rounded. He falls from the ladder. The top legs are now square. (00:07:15)
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.
Continuity mistake: At the end of the episode, watch the colour of the time-machine inventor's outfit. You can see it's light blue when he pulls the lever, but when he gets the Flintstones and Rubbles back to the fair and asks them what happened, his outfit is a darker shade of blue. It then changes back to its lighter shade as before.
Continuity mistake: Towards the end of the episode when the time-machine inventor pulls the lever on the machine, three lemons appear and he says "Wow, Jackpot!". But in the next shot, when the Flintstones and Rubbles run out of the machine, the lemons have vanished.
Continuity mistake: When Fred pays the man at the hamburger stall 'two rocks', he places the money on the counter. When we see a close up of the money, one rock is behind the other one, but in the very next shot the two rocks are now lying side by side.
Continuity mistake: When the man at the hamburger stall gives Fred his 'brontosaurus burgers', he serves them on a tray, but just a few shots later the tray is nowhere to seen.
Continuity mistake: After Wilma and Betty have pulled Fred and Barney out of Kitty's Place, the background behind them initially has a yellow saloon but then changes to a blue building in the very next shot.
Continuity mistake: When Kitty puts the coin in the juke box, the position of the mallet used to hit the bird on the head changes between shots.
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