Lentilus Bataiatus is talking to Gracchus after having being flogged. He is having his wounds treated and the scene is very jumpy onscreen. [This 'mistake' is not visible in any version of the film I have seen, including my own DVD copy. Perhaps you have seen a badly made print of the film?]

If Crassus wanted Spartacus alive after the battle, why didn't he just get him to give himself up by having Varinia and her child go among the surviving prisoners.beats nailing them all up. [Character Choice. Not a mistake.]

In the scene where Gracchus is giving money and travel permits to Batiatus and Varinia, he mentions that one of his innumerable cousins is the Governor of Aquitania. Aquitania would not become of a province of the Roman Empire for more than 40 years following the time of Spartacus' revolt. [The key word is 'innumerable'. Gracchus' "cousin" is not a Roman citizen, and the title 'Governor' was a misnomer - he was more correctly a warlord or provincial dictator. Aquitania held very close links with the Roman Empire for centuries before it was annexed, and intermarriage and cross-migration was very common.]

In the scene when Spartacus is detailing on a map how he intends to invade Rome, he is reading the cities on the map of Rome. In the scene immediately prior to that, we learned he cannot read. How did he learn so quickly ? [It should possible for an illiterate person to memorize a map by its contents. The city names will have been pointed out by one of his aides (or another freed slave) who could read, and all he had to do is to memorize the locations.]

If you look at the legions of Roman soldiers at just about any point in the film, they're wearing wristwatches and trainers. [There were no such thing as 'trainers' in 1960, when the film was made. The Roman soldiers are all correctly attired. None of them are wearing inappropriate footwear and though their decorative metal and cloth wrist protectors might look like watches in some shots, that is not what they are.]

In the scene at the gladiatorial school Crassus's protege is introduced as Marcus Publius Glabrus. Later in the Senate, he's called Publius Marcus Glabrus. [Patronymic names were sometimes used in this way.]

At the end of the film, Spartacus is crucified along with all of his surviving men. In reality, Spartacus was killed during the final battle against the Romans. [The film is not intended to be a historical documentary - most of it bears little resemblence to the known facts. In fact the real Spartacus disappeared during the final battle in Calabria. Nobody knows what happened to him. Realising that that would make a pretty dull ending to the film, the scriptwriters fictionalised his death (and much of his life, too).]

This is more of an omission rather than a mistake. One of the reasons why Spartacus and his army was defeated was the internal strife between Spartacus and his lieutenant, Crixus. According to Greek historians, Appius and Plutarch, Spartacus wanted his army to leave the Italian peninsula and go to Gaul so the army can be disbanded. After disbanding, Spartacus wanted the slaves to go home to their countries of origin. However, Crixus wanted to stay in Italy and keep on pillaging. The Roman generals used this internal strife to their advantage and defeated Spartacus' army. The movie makes no mention of this very historically significant internal strife. [The film never pretended to be a historical documentary. In fact the story of the real Spartacus is completely different to the film, which is an epic drama, and a largely fictional one at that.]