During the gladiator fight, when Pollo chops off a gladiator's head with a shield, the head is still attached to the body in the next shot. Later in the fight the head is chopped off again.
The white parrot when Vorenus sits as magistrate is an Australian The Sulphur-crested Cockatoo. The Romans didn't wander that far in search of exotic birds.
The Germanic Gladiator big two handed sword later used by Vorenus is actually a Chinese Dadao though it is a very basic weapon the form in which it appears on the series did not existed at least until the 19th century.
Though the series is known for its historical accuracy, several weapons are shown out of time, such as Roman shields from later periods, daggers from much previous times, Roman swords with modern fittings and even a Chinese sword from the 19th century.