When Mark Anthony is retreating back to his palace he's dressed as a Roman soldier but once he's in the palace he appears to be dressed as an Egyptian alongside Cleopatra.
When Vorenus & Pullo are talking about leaving, they mention the Romans controlling the ports in Upper Egypt and to travel south. However, Upper Egypt is in the south and Lower Egypt is in the north. This is based on the direction of the Nile, which flows from south in the Highlands to north forming the Nile Delta before feeding the Mediterranean Sea.
Caesarion was 17 years-old when Octavian seized control of Alexandria. Prior to Octavian's invasion, Caesarion was sent by Cleopatra out of Egypt to escape. However, Caesarion's guardians brought Caesarion back to Alexandria (possibly by promises made by Octavian) where Octavian had Caesarion murdered and uttered the infamous line, "Two Caesars is one too many." Caesarion never left Egypt alive. Strong evidence also suggests that Caesarion was, indeed, the son of Julius Caesar.
When offered terms for surrender, Mark Anthony tells the ambassador that "Octavian can take his terms and shove them up his ass". This kind of expression wouldn't have been used and wouldn't be part of spoken language during this era.
At about the 30 minute mark, when Cleopatra falls prostrate before the supposedly dead Mark Antony on his throne, Antony's head moves ever so slightly.
The title of the episode is listed in Latin and English as "De Patre Vostro (About Your Father)" and is taken from the final words of the episode spoken by Titus Pullo to Caesarion, "Listen, about your father..." However, in Latin, such a statement should be "de patre tuo" with the singular possessive since Pullo is talking to only one person (Caesarion) when he says it.
The action that takes place during "Rome" covers huge lengths of time, yet the characters do not age accordingly. For example, Season 2 begins with the assassination of Julius Caesar (44 BC) and ends with Octavian's capture of Egypt (30 BC) a period of 14 years, and yet during the course of the season, no aging takes place among the characters (with the exception of an actor change for Octavian)...take particular note of the children of Lucius Vorenus, who are children in 44 BC, and by the end of the show have most certainly not aged 14 years (they are STILL children at the end).