This has been bothering me something terrible since I noticed it yesterday.
Wilma Flintstone and Barney Rubble have only black disks for eyes. Fred Flintstone and Betty Rubble have eyes with whites and pupils. Even their pet Dino has whites and pupils.
However, the way I always took it was that it provided a nice contrast between whichever two characters were together in the scene. Most scenes featured only two characters, and the breakdowns were usually:
[ul]
[li]Fred and Wilma[/li][li]Wilma and Betty[/li][li]Fred and Barney[/li][li]Barney and Betty[/li][/ul]
This means that no matter the scene, you end up with one cartoony-eyed character and one disc-eyed character. It’s more visually pleasing that way.