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.
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.
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.
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.
One of Gohan's energy attacks knocks out a number of Recoome's teeth. From that point on, the amount of Recoome's teeth in his mouth becomes inconsistent between shots. Sometimes he's shows with a whole mouthful of teeth, other times he only has a few remaining.
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.
King Kai, Bubbles, Elder Kai, and Gregory are all seen on Earth during the 2008 special. But they're dead and have no way of coming to Earth - there's even a line in the Buu Saga about how Elder Kai gives his life to Goku because he is unable to come to Earth.
Tien's failed suicide attack cracks Nappa's armor. When Nappa charges at the Z-Fighters (when Vegeta orders him to stop) his armor is in pristine, undamaged condition. In the scenes that follow it's broken again. (Unlike many other animation errors, this was not corrected in Dragon Ball Kai.)
French dubbed version: In the beginning of the Garlic Jr saga, Gohan claims that he is 5 years old. However, he should be much older since he was 4 in the beginning of the series, and several years have passed since then.
French dubbed version: A lot of the characters are never named, yet somehow other characters know their names. This happens with for example Vegeta, Ginyu and Jeice. None of them ever state their names, yet several episodes later, the others know what they are called.
French dubbed version: When Vegeta suggests creating a Genki Dama ball during their fight with Buu, Goku doesn't know what a Genki Dama is. This makes no sense, since he has already used it numerous times by this point.
French dubbed version: About half the time, the attack names are all wrong. The Solar Fist and Neo Tri-Beam are almost always confused, the Destructo Disk is called differently every time it's used, and nearly every attack is called Kamehameha at one point. Also, a lot of times the attack names are never even used, and are replaced with random trash-talk.
The fusion of Goku and Vegeta is called Vegito, which is a cross of their Japanese Saiyan names, Vegeta and Kakarotto. Even though the dub shortened the latter's name to Kakarot, they maintained the name Vegito for the dub, which confused many fans. The American manga corrected this problem by calling this fusion Vegerot.
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.
The original Pioneer/Saban dub got Vegeta's artificial moonlight explanation horribly wrong. Vegeta tells Goku that Bardock was a scientist and developed the technique. This is wrong; Bardock was a very strong lower-class warrior who was obviously no scientist. Note that FUNimation has long since redubbed the early episodes, and this inaccurate quote has long since been replaced with a fairly accurate description of the phenomenon.
ENGLISH DUB: During his fight with the transformed Vegeta, Goku comes to the conclusion that the transformed Vegeta is the one who destroyed the world martial arts stadium when Goku was just a boy. This conclusion is absolutely absurd since Vegeta had never before visited Earth (corrected in FUNimation's redubbed version). This error is also present in the French dub and all the other European dubs that have been based on it.
Planet Vegeta was destroyed by Frieza, but when King Kai tells Goku a history of the Saiyan race, he tells Goku that the planet's Kami destroyed the planet with a meteor. The meteor story was the widely-believed story around the galaxy, but an all-knowing galactic god like King Kai should have known better (though he could have made up the story to keep Goku from going after Frieza.)
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.
In the original Pioneer/Saban dub, when Goku dies the first time and the corpse vanishes, Piccolo says Kami had something to do with it. Krillin asks "Who's Kami?", despite the fact that Krillin had actually met Kami at the 23rd Tenkaichi Budokai (corrected in FUNimation's re-dubbed version.)
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).
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.
During one of the scenes right before Frieza 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.)
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.