All of the senators have names from other Hollywood epics, not actual historical figures. See more...
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Factual error: When Maximus walks through the wheat field it is obvious (to a botanist) that the wheat shown is an octaploid variety which was developed in the 1950's for the Green Revolution. The type of wheat grown during Roman times can still be found in many areas too, so it's not like the filmmakers can't find it.
Revealing: In the beginning of the film at the major fight sequence. When you see the Romans shield themselves with the rectangular shields against the barbarian's arrows and then they charge at each other. If you look closely enough, you can see two Roman soldiers standing there having a great laugh, one pointing a sword smiling, and the other one staring at the ground laughing to his heart's delight.
Revealing: After the first battle in the Colosseum (The Battle of Carthage), Commodus decides to meet "The Spaniard" in the arena. When Quintus (the head of the Praetorian Guard) is telling the slaves to drop their weapons, we can see one of the spectators hiding a plastic bottle of water (right upper corner of the screen).
Continuity: After Maximus comes out of the tunnel after leaving the gladiator quarters, he sees his friend Cicero. Maximus makes a bird noise to get his attention, Cicero sees him and in an attempt to warn him he yells "Maximus." He startles his horse which runs away but a noose is around his neck so he is pulled off the horse and left hanging there. As soon as the horse leaves him and he starts swinging his hands you can see they are not tied. Then when Maximus runs up to him and holds his feet up to try and save him his hands are tied up.
Factual error: During a meal in the gladiatorial school, Juba is shown eating with a metal spoon. Slave-gladiators almost certainly only ate with their fingers, wooden spoons, or wads of bread to sop up their food. They never would have access to metal spoons that could be sharpened and used to attack the guards keeping watch over them.