Tavius is seen clutching his cross while the TARDIS crew make their escape back to the Villa. Christians during Nero's time did not use a cross to indicate their faith, they used the ichthys ,the stylized fish you often see on modern cars.
A close-up reveals that the coins Nero uses to pay his torch bearers are in fact metal washers.
During the burning of Rome, the flames are not to scale with the model of the city. Thus revealing that an inlay shot is used to create the effect.
Nero talks about alligators, but they were not known to Europeans until the discovery of Florida more than 1400 years later.