GLADIATOR
Historical setting: 180 AD
When we first see Commodus he worries over whether or not he will be named heir. Historically, Commodus was named as co-ruler of the Empire when he was 16 in 177 AD, and was therefore already guaranteed to inherit the title of Emperor.
Historically Commodus accompanied his father to the front lines, and therefore he wouldn't have missed the battle as he did in the movie.
When Marcus Aurelius died suddenly, Commodus and the Germans came to terms, so there was not one main final battle that ended the German threat. Had Marcus Aurelius not died, he would, most likely, have continued to annex German territory north of the Danube, but Commodus may have been the wiser for calling off the costly expansions.
There was no way Marcus Aurelius could have bypassed his son as heir unless he had ordered Commodus killed.
Until 180 AD, only one other son had inherited from his biological father. All other men inherited from men who had adopted them, or from siblings, or strength of arms. Hadrian's adoption by Trajan was widely disputed, and he was forced, for years, to cement his ties to his adoptive father. Maximus could not have inherited the Emperor title simply because Marcus Aurelius wished it.
The word Coliseum is spoken a few times in the movie, but it was only called that in the middle ages. To the Romans it was the Flavian Amphitheatre.
In the movie you can clearly see men and women sitting together in the Amphithetre's seat, when in truth they were strictly separated, women sitting in the far back.
Thumbs up and thumbs down are more modern hand signals. When the Romans called for someone's death they gestured to the neck, making reference to how the killing blow would be delivered.
The Roman Republic officially ended in 27 BC when Augustus was proclaimed Emperor. By 180 AD it was a distant past that not many people envisioned coming back. Certainly not Marcus Aurelius, who'd already named his son heir in 177 AD.
Commodus ruled as sole Emperor from 180-192 AD.
Lucilla and the senator's coup was attempted in 182 AD, and failed miserably.
Though he sometimes went into the arena to fight as a gladiator, he was strangled by his mistress Marcia's lover, who was a gladiator.
Rome did not suddenly become a Republic after Commodus' death.
After Commodus' death the empire descended into a civil war, lasting from 193-197 AD. A man named Severus eventually came out on top. Severus ruled from 197-208 AD. Neither he, nor Commodus, were the last Emperor.
Sources
Encyclopedia Britannica.
Macropaedia. Volume 11, pg 492 and 493.
Micropaedia. Volume III, pg 41.
Goldsworth, Adrian. Roman Warfare. London: Cassel & Co, 2000. Pg 13.
Ramage, Nancy and Andrew Ramage. Roman Art. New Jersey: Prentice Hall, 2001. Pg 156-160, 336.