Factual error: Before the eruption, we see Mount Vesuvius with a crater. Mount Vesuvius did not have a crater prior to the eruption in AD 79. This can be seen in a fresco depicting Mount Vesuvius found in Pompeii.
Continuity mistake: In the scene where Corvus kidnaps Cassia and is racing through the city on his chariot, the street he is travelling down is completely devoid of rubble, bodies, and anything else that was already shown to be strewn across all of the streets.
Factual error: The people of Pompeii are frequently referred to as not being Roman citizens. They very definitely were Roman citizens with full rights. You didn't have to come from the actual City of Rome to be a Roman citizen, as is implied in this film.
Factual error: In a brief scene showing a map of Europe as it was in 79 AD, complete with Latin. Rome is displayed with the Flavian Amphitheater (Roman Colosseum), however, Pompeii was destroyed in 79 AD and the Colosseum did not open until 80 AD and was not finished to look as the Colosseum we know it and as shown on the map in the movie, until many years after that under the rule of Domitian, the brother of Titus.
Continuity mistake: In the scene after The Celt defeats the big Thracian in a fight at the slaves' "new home", Master Graecus comes to get Bellator's explanation about the fight. After Graecus leaves, Bellator says "I'll remember you, Celt." Before Bellator says that, The Celt's left collar is below his shoulder. Just after Bellator says that, the camera cuts to show The Celt and his left collar is now on his shoulder. (00:19:25)
Factual error: There was no Roman law saying a gladiator had to be freed after a certain number of victories and no gladiator would have believed there was. It was entirely up to his owner whether or when he was freed.