Saga of a Star World (1) - S1-E1
Plot hole: Apollo takes Adama down to the surface of Caprica aboard his Viper, yet the Viper is a single-seat fighter. This is the only time the single-seat craft is used to carry two people (though there is no shot of the two aboard - it is simply shown landed with the two characters nearby).
Suggested correction: It was 2 seater Viper training aircraft.
Plot hole: In the first season, Lucy Ewing had an affair with Ray, the farm hand at South Fork. Several years later, it was revealed that Ray was actually Jock Ewing's illegitimate son, making him Lucy's uncle. However, the subject of their affair was never raised, even though they surely would have been at least somewhat traumatized upon learning of the accidental incest.
Plot hole: Chrissy is pushing her baby Jay in her pram into the school playground. Justine and Luke call out to her from an upstairs window, then come out to meet Chrissy. They come down from an upstairs floor to the playground in five seconds, which is not enough time.
Suggested correction: This might be a mistake, but it's not really a plot hole. The plot of the episode isn't broken because two characters travel a short distance too quickly. The time they take isn't a key part of the plot; it has no impact on anything.
Plot hole: Michelle and the girls are winning at Baccarat every time due to a system where they know the cards in advance by seeing through them. However, all betting in that game is done before cards start coming out of the dealer's card chute onto the table. So even with their cheating system, they realistically couldn't always win, as the cards are not already face down on the table.