Factual error: The future emperor Augustus is called Octavian, an English modification of Octavianus. However, before being adopted by Caesar (which happened after Caesar returned from Egypt) his name was Octavius. When he was adopted he took the name Gaius Julius Caesar Octavianus, and at that point the English version of his name is Octavian, but before the adoption he did not have that name. On the show they are thus calling him by a name he did not have at the time.
Factual error: The eagle was the standard of each legion, not Caesar's personal standard as stated in the series, even by Caesar himself (to Brutus). Also, the Aquilifer (eagle bearer) was traditionally bareheaded - unlike the other standard bearers, he did not wear a bearskin or a helmet.
Answer: According to wikipedia, Pompey's children are all from his third wife, Mucia Tertia. Julia is his fourth wife. See: http://en.wikipedia.org/wiki/Pompey#Marriages_and_offspring.
Myridon