During several episodes captive birds are shown. There are Macaws and Amazon parrots from America, and cockatoos from Australia. Since the continents these birds came from were unknown to the Romans, they would not have been able to travel there and bring these animals back to Rome with them.
The words Domina and Dominus are practically the only Latin words the cast uses regularly. Nevertheless, as they are always used as vocative, the masculine form should be Domine. More than that, the spoken Latin of the higher classes is inadequately close to ecclesiastical late Latin.
Several historical changes were made to move the story along. Octavian was in Illyria undergoing military training when Caesar was killed. Livia was actually Octavian's third wife and she had two sons when she married Octavian; Tiberius and Drusus. Drusus was married to Antonia, the daughter of Marc Antony and Octavia and was the grandfather of Caligula and the father of Claudius. Octavian had one natural child, Julia, by his first wife. Julia was married at one time to Tiberius.
The series implies that the break between Caesar and Pompey happens after the death of Julia, Caesar's daughter and Pompey's wife. In reality, she had been dead for several years by the time of Caesar's conflict with Rome.