In numerous episodes throughout the series, the capacity of passengers in both Fred's and Barney's cars changes back and forth from seating two passengers to four passengers.
The bosses of Fred and Barney both have a first name of George, but their last name keeps changing from Slate to Granite, back & forth throughout season one.
Dino changes colors from purple to red throughout the series. Plus, he is blue in the opening credits of seasons 1 and 2.
Characters are shown having telephones and televisions, even though those did not exist during the prehistoric days.
During the closing credits, when Wilma is shown in bed sleeping, she has no mouth.
All throughout the series, the cars are run by foot. If this is the case, why do the gas stations exist? Often the only thing their feet do is get the car going.
Since the windows of the Flintstones' house are quite big and do not have any glass, why does Fred keep banging the door after being kicked out by the saber-tooth cat? He could easily follow the cat's example and enter through the window.