Despite having little physical resemblance to any known representations of the historical Caesar who was balding, the series aims to present him in an authentic fashion (as opposed to an accurate one).
The story starts in 52 BC as Caesar receives news of his daughter Julia's death; historically, Julia died in 54 BC. Additionally, no mention is made in Rome of his mother Aurelia Cotta, who died months after Julia. There is nothing in the historical sources to suggest that his affair with Servilia ended, as is depicted in the series.
Caesarion was likely Caesar's son with Cleopatra. The events of the episode Caesarion insinuate that he may actually have been fathered by soldier Titus Pullo. Though Caesar is shown presenting his newborn son to his army at the end of this episode, historically Caesar was already back in Rome by the time Caesarion was born.