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.
Much of the interior decor of Cleopatra's palace in Alexandria is anachronistic. Some items of furniture are exact copies of those found in the tomb of queen Hetepheres I (c. 2600 BC). Statues seen on Cleopatra's barge are copies of one found in the tomb of Tutankhamun (c. 1330 BC).
Although we learn that Cleopatra is supposed to be the incarnation of the Egyptian goddess Isis, everybody except Taylor pronounces it "Isis." Taylor pronounces it "Isis" if the line is not dramatic and "Ises" if it is.
When Cleopatra enters Rome on her sphinx, there is a dark red marble column to her right and close to the arch. In the breathtaking shot of the entire sphinx from the side, the sphinx goes past the column but the arch is nowhere to be seen. When the sphinx stops, the column is roughly even with the sphinx's shoulder. Given the amount of room between Caesar and the arch, the sphinx probably never comes completely through the arch.
When Caesar is saying goodbye to Cleopatra in Alexandria before sailing back to Rome, one of his aides hurries him by warning, "Caesar, I'm afraid the tides will soon be against you." 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.
Cleopatra's arrival and procession would not have entered the Roman Forum itself, as portrayed in the movie, since during the Republic, all foreign rulers were prohibited from crossing the Pomerium, the sacred boundary of the city, into Rome proper.
Following the assassination of Caesar, Agrippa is depicted in two scenes as seated in the Curia wearing a senatorial toga. In reality, Agrippa was a hereditary member of the Equestrian order and therefore prohibited under Republican law from either non-invitational attendance in the Curia, or the wearing of patrician insignia. Likewise, prior to Caesar's death and his succession, Octavian is seen seated in the Curia, when he himself would only appear if he was invited.
The claim that Caesar wanted to be made Emperor is false. Though Caesar was hailed by the title of imperator during his lifetime, the Roman sense of the term was far different from that denoted by the word "Emperor," being used to describe a great military commander rather than a supreme monarch.
The scenes of Cleopatra's magnificent entry into Rome are enacted in front of (and through) a detailed and life-size replica of the Arch of Constantine, built in AD 315 - more than three and a half centuries after the event.
Caesar picking up his child Caesarion in front of other Romans would not have been sufficient to have the boy become a Roman citizen, and consequently Caesar's heir. For that, both parents would have had to be Roman citizens themselves, and Caesar never acknowledged him as his son.
Caesarion is depicted as being around the age of 10 when he leaves Egypt for his own safety. In reality, Caesarion was at least in his early teens after Cleopatra's death, and he also didn't leave Egypt, instead taking Cleopatra's place as King of Egypt.
When Cleopatra is delivered in the carpet, Caesar asks Apollodorus to flip the rug over so it will be wrong-side-up. But flipping over a rolled carpet doesn't change which side is up, just the direction it will unroll.
When Rome declares war on Ptolemaic Egypt, Octavian is portrayed exiting the Curia and spearing Cleopatra's ambassador Sosigenes of Alexandria. There is no historical basis for this depiction, or even Sosigenes being a prime functionary for Cleopatra's regime (he was an astronomer).
During the thunderstorm on the evening of March 14, 44 B.C., lightning flashes twice. But it's the same lightning flash repeated. (It's also blurry and looks cheap.) And the flash doesn't flow; it appears as a complete image. Also, the thunder happens at the same moment we see the flashes. Finally, the thunderclaps are identical, which in a way makes sense since the lightning was, too.
When Cleopatra is presented to Caesar in a rug... the rug is rolled up and flat. But
as the rug is unrolled (offscreen) Cleopatra miraculously pops out. Even if Liz
Taylor was a size zero... there is no way a human would fit that flat into a rolled up rug.
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.