The legionaries are dressed like the Imperial Legions with lorica segmentata armour (plate in sheets held together by joints) and not as the post marian reform units they really were at that time that would wear a sort of chainmail armour or "Lorica Hamata". It is contested by some historians even that the Lorica Segmentata never reached widespread use and even maybe only functioned as a ceremonial type of armour.
In any case the first known (minor)a ppearance of this armour is in 19 BC, some time after the events portrayed in the movie.
No mention is made of Cleopatra's three children by Marc Antony, twins Alexander Helios and Cleoptra Selene II (born 40 BC), and Ptolemy Philadelphus (born 36 BC). After Octavian conquered Egypt, they were sent to Rome, where they would eventually be raised by Octavia Minor, Octavian's sister and Marc Antony's wife. Marc Antony also had at least five children before he fell in love with Cleopatra, none of whom are mentioned.
Cleopatra mentions the Octavian is not Caesar's 'flesh and blood'. Octavian was in fact, Caesar's grandnephew, the son of Caesar's niece Atia (though Caesar introduces him as simply his 'nephew', whether this is a goof or just simplification on Caesar's part is unclear)
Arsinoe was captured by the Romans, but not strangled by Cleopatra's guards in Egypt as shown. She was taken as a captive to Rome in 46 BC and remained alive, living in a Roman temple until 41 BC, when she was executed on Marc Antony's orders.
Cleopatra actually had two brothers, Ptolemy XIII and Ptolemy XIV, both of whom she was married to. Ptolemy XIII was her first brother/husband, but with the help of Pothinus, forced Cleopatra to flee Egypt with their sister Arsinoe. Caeser, who at this point was already Cleopatra's lover, reinstated her to the throne. However, Ptolemy XIII allied himself with Arsinoe against the pair, but Roman reinforcements forced them to flee the city, and Ptolemy XIII drowned attempting to cross the Nile in 47 BC, aged around 14-15. Cleopatra was then married to her second brother/husband, Ptolemy XIV, who was co-ruler with her (though she retained the power) until shortly after the death of Caesar, when he died (possibly murdered) at the age of about 15 and was replaced with Cleopatra's 3-year-old son Caesarion (Ptolemy XV).
During the battle within the walls of Alexandria, Cleopatra is running to save the burning library and is chased down by a soldier on a horse. Cleopatra uses her own spear to flip him into a pillar. When he hits the base of the pillar, it moves, revealing that it is a loosely attached prop.