In the Raditz fight, Piccolo has red blood. In all subsequent fights, he has purple blood.
In the English dub, it is said that Planet Vegeta was destroyed three years ago, but it is later changed to twenty years ago (the latter is accurate to the Japanese original.) Interestingly, even when they did the "uncut dubbed" version on Cartoon Network, in the early Raditz episodes they still used the inaccurate "three years" quote.
In Freeza Saga's flashbacks, Vegeta is in the bowels of Freeza's ship when Freeza destroys Planet Vegeta. In the Bardock TV Special(faithful to the manga), though, Vegeta is on a far away world when this happens.
When Goku visits the Snake Princess, he gets her digestive juices on his clothing, which causes some damage to them. Yet when he's running on the Snake Way in the next episode, his clothes are undamaged.
In the 2008 special, the press is apparently aware of the threat of Majin Buu, despite the fact that the public's memories of the conflict were erased.
During a scene when Trunks fights Cell (back in his own timeline), the time capsule misspells "Capsule Corp" as "Capsule Coop."
At the concession stand just outside the Stadium Yamcha is playing baseball at, "hamburger" is misspelled (as "hanburger.")
During one of the scenes right before Freeza transforms into his second form, Vegeta is drawn for one frame with the shoulder-padded armor he was wearing earlier in the saga (he switched to shoulder-less armor after the Ginyu fight.)
When Goku's ship lifts off en route for Namek, the word "Capsule" on the side of the ship is misspelled (as "cpsule"). (Unlike many other animation errors, this was not corrected in Dragon Ball Kai.)
A hole is ripped in Yamcha's orange gi due to Android 20 slicing through his chest with his palm. But after Goku's friends move Goku to Master Roshi's house to recover, the hole in Yamcha's gi vanishes.
During a scene following the Raditz battle when Piccolo is talking to Roshi, Krillin, and Bulma, he is drawn with two arms despite the fact that Raditz's attack severed his arm. He didn't regenerate it until the next episode, either.
For one frame during the Raditz battle, the "Kame" patch on Goku's gi is the same orange color as the rest of his gi.
The fusion of Goku and Vegeta is called Vegito, which is a cross of their Saiyanjin names, Vegeta and Kakarotto.
During the Namek saga, when Gohan is trying to hide a Dragon Ball from Vegeta, Vegeta notices the radar in Gohan's hand and asks what it is. Gohan lies that it's a clock, to which Vegeta responds that Earth technology must be primitive if clocks are so big. However in a few European dubbings, based on the series' French versions, Gohan doesn't call it a clock, but a monster, prompting Vegeta to respond that Earth monsters sure are small. But this translation makes no sense, as the radar is clearly a mechanical gadget, so there is no way Vegeta would believe it to be a monster.
In the twenty year gap between the Bardock Special and the Freeza Saga, Freeza and his henchmen don't age, yet the Saiyanjin characters clearly do.
The Future Z-Fighter death scenes in the series (in a flashback Perfect Cell and Future Trunks have) contradict those seen in the Trunks Special.
French dubbed version: In one filler episode, Vegeta goes around looking for a certain person named "Cachalote". This is really an erroneous translation of Goku's birth name Kakarot. However in this dub, Vegeta always calls Goku by his Earth name ("Songoku"), and it is never explained who this Cachalote is supposed to be.
Piccolo claims that a long as his head is intact, he can regenerate from any injury. For example, he can regrow his arm or put himself back together after being broken to pieces. Yet he is gravely injured at several points during the series when his chest is hurt, and his head is intact during his first death, but still dies.
It is a rule that only people who have performed great deeds and are deemed worthy retain their bodies in afterlife, while the rest are turned into cloud-like ghosts. Yet evildoers who appear in Hell all retain their bodies. However, this mostly only happens in pointless filler episodes or scenes that were exclusive to the animated series (and thus not part of the original storyline presented in the manga).
French dubbed version: Vegeta claims that Saiyans can transform into anything they want. This is not true. They can only turn into giant apes and a few select Saiyans can become Super Saiyans.
French dubbed version: When first achieving the Super Saiyan stage, instead of saying "I am the Legendary Super Saiyan", Goku says "By the power of King Kaio, transformation!" It seems that the translator has confused the Super Saiyan stage with the Kaioken technique. This error was carried over into other foreign dubs based on the French dub.
In some European dubs, the "-ha" from the end of the Kamehameha attack is always left out and replaced with random shouting. This translation error has become widely accepted in these areas, so in certain countries, the attack name is recognized as "Kamehame" by most people.
French dubbed version: the Snake Way is said to be 100 kilometers long. It is actually a million km long, hence why it takes Goku so incredibly long to traverse it. If it really was 100 km long, he would have made the trip in no time.