Cleopatra refers to Octavian as "Octavius Gaius Julius Caesar Augustus." The senate also refer to him as "the August." However, Gaius Octavius wasn't given the name "Augustus" or made emperor until 27 BC, three years after Cleopatra's death.
In one point Caesar talks to Cleopatra about Rome's interest in Egyptian maize. Ancient people had no idea about it, since maize was originally cultivated in prehistoric Mesoamerica and spread worldwide only in the 15th and 16th centuries.
When Caesar is saying goodbye to Cleopatra in Alexandria before sailing back to Rome, one of his aides hurries him by warning, "You will miss your tide." In fact, Mediterranean has no tides, or more precisely, its tides are so minimal that they don't affect navigation. No ship sailing from a Mediterranean port would have to worry about catching a tide.
When Caesar leaves for the Senate just prior to his assassination, there appear to be brown leaves on the ground. The event in question took place in March, and leaves blown down by the storm would likely be green.