The opening tells us that the date is 358 BC, yet the cultures and governments depicted in the movie are typical of a much earlier time, possibly even 1358 BC. One of the most telling details is that Eurystheus is called the King of Athens, an office abolished at least 400 years earlier when Athens became a republic.
After Hercules' fight with the wolves, he is bitten in numerous places (neck, leg, arm), yet when he stands after the statue falls, there is no blood on his neck nor are there are bite marks. [He also showed a remarkable lack of pain]
When Hercules' was being charged by the villager, he clearly breaks the tip off Atalanta's arrow. After punching the villager, the arrow embedded in his forehead has a longer shaft than was broken originally.
The movie features numerous characters from mythology and legend, using the Greek names. Except for the title character who is referred to by his Roman name Hercules rather than Heracles. Nearly all movies do this because his Roman name is much more recognizable in pop culture and is a sensible marketing choice. It can be considered a translation of what the characters were really saying.
In the prologue, the Nemean lion's head alone outsizes Hercules entirely, yet he later wears the head as a helmet and it is relatively small. The prologue was told from the subjective viewpoint of Iolaus, who is later shown to be fond of telling tall tales and stretching the truth about Hercules' past.
After Hercules saves his companion from a flaming spear, he throws a soldier down a hole. When said soldier hits the rocks before falling down, you can see the prop rocks shrinking under the stunt actor's weight.
Some close-ups of Hercules facing Rhesus' army have been flopped. The rectangular Thracian shields have a space top-right for a spear but in at least two shots the soldiers behind Hercules have a space on the top-left of their shields.