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.