At the quiz it is claimed that every Roman soldier wears a leather skirt. This is totally nonsensical.
The Roman soldiers appearing in this episode are wearing armor and helmets from the 1st century AD. During Julius Caesar's lifetime, most common legionaries would have been wearing a chain mail armor and a simple bronze helmet. Plate armor wasn't used at the time at all.
Of Caesar's centurions at Rubicon river, three of them wear handlebar mustaches. These were never in fashion with the Romans.
The room where Caesar meets Cleopatra has windows with a round arch, a so-called Roman arch. As the name implies, these windows are a Roman type invented in Italy, making it very unlikely that Alexandrian buildings would have had these during Caesar's lifetime.
When murdered in Rome, Caesar is wearing a red toga. Only augurs wore red togas. Most likely, Caesar would have been wearing a purple toga, which he kept wearing after his triumph.
Caesar is constantly addressed as "highness", despite not being royalty.
Caesar plans to wear red shoes, which one of his officers explains as a sign that he wants to be a dictator. Although the red shoes together with the purple toga were originally a sign of the king of Rome, they were bestowed on any Roman general receiving a triumph. Only when Caesar didn't stop wearing these items, it seemed like a sign that he wanted to become king - not a dictator, which he already became in 49 BC, 4 years before his triumph.