Corrected entry: Quintus Pompey introduces himself as Quintus Valerius Pompey. If he is the son of Gnaeus Pompey, then his name would be simply Quintus Pompey, not Quintus Valerius Pompey. Adding the name 'Valerius' makes him a member of the gens Valeria, i.e. an entirely different family.
Corrected entry: There was no Roman named Marc Anthony, the man who was a friend of Caesars and later husband of Cleopatra was named Marcus Antonius. If they called him Marc Anthony at all times in the series that wouldn't be a mistake, since it would be "modernized" language, but in this episode they at one point refer to him as Marcus Antonius. If they acknowledge that this is his name it is an error for them to call him Marc Anthony in other scenes because it makes no sense.