Just after 20' Caesar, replying to Agrippa, states "I only have the one sister, Agrippa." This is not true, since at the time (43 B.C., shortly after the battle of Mutina) Caesar had two living sisters: Octavia Major and Octavia Minor. Octavia Minor is the only sister appearing in the series.
At a time two mounted roman soldiers are using stirrups. These ones did not arrive in Europe before the VII centuries.
In Season 2 - Octavian has shown to be aged significantly with time but Lucius Vorenus's children did not age at all.