When Goku bites Piccolo Daimao's hand and makes him bleed, his blood is red. But in DBZ, all Namekians have purple blood.
For the first few episodes that feature the Red Ribbon army, their logo undergoes several slight changes.
On the airship Pilaf flies on with Piccolo Daimao, the name "PILAF" on the side of the airship appears and disappears between scenes.
When the Red Ribbon Army opens fire in Suno's house, they destroy the "toilet" sign on the bathroom door. Yet in all subsequent scenes after Goku has defeated this division of the army, the sign is restored.
On General Blue's wristband, the writing is alternately white/black between shots.
For one frame when he's running in the pirate cave, General Blue's name in his wristband is misspelled (as "bule.")
At the 23rd World Martial Arts Tournament, one spectator's shirt misspells Budokai as Budoukai.
Boss Rabbit's overcoat is green, but in two close-up shots of him it's black.
One thing that seems to cause confusion amongst people posting goofs on the site is the status of the moon. People claim Master Roshi destroyed it in the original series but it was back in Z when Piccolo destroyed it. The original Dragon Ball briefly states, however, that Kami restored the moon himself.
When Master Roshi is introduced he knows nothing about the Dragon Balls. Yet later in the series, he tells Goku and company an extremely detailed story about their origin.
When Goku beats Tien in the 23rd World Tournament, the announcer says Goku will go on to fight Piccolo Jr. in the finals. However, at this point the Shen/Piccolo Jr. fight had NOT yet taken place. Therefore the announcer couldn't have known this.