When Fred is in the Hot Coal race with Turk Tarpit, Fred's Clothes turn into Barney's clothes for a second.
Fred and Barney's cup of coconut juice disappears.
When Astro steps on a stick in Bedrock he was walking on grass, but in the next shot, he is walking on dirt.
Elroy says he has it set for future, but a closeup of the time machine's switch shows it set to PAST. A later shot shows the switch falling from the Future position to Past.
When Judy has a fight with Cosmo, she slams the house door open, squashing her dad behind it. In the next shot, the door is suddenly shut with George on the outside as the door falls off its hinges into the house with George on top of it.
When Judy is taking a shower at the Flintstones house, she turns the shower on with a bone in her hair, but when the elephant comes, her black bow suddenly appears.
When the time machine activates, George appears to be saying "Three... two... one..." but no sound is coming out of him.
When the Jetson's return from the past, Mr. Spacely is on the floor crying and throwing a tantrum. When George comes in and picks Mr. Spacely up off the floor for a hug, you can see Mr. Spacely's mouth move for two more cries but no noise is heard.