When Phil admonishes Hercules, "Don't let your guard down because of a pair of big goo-goo eyes," he's clearly mouthing the word "blue" instead of "goo-goo." Meg's eyes were originally going to be blue, but later on they were changed to purple to match her dress.
During the scene with Megara and Hercules by the fountain, the armless statue at the end changes into a man and a woman holding a ribbon between scenes. Also, during that scene, Meg and Hercules change locations around the fountain and the statue rotates with them.
When Hercules destroys the marketplace near the beginning of the movie, the pillars start falling outwards from the center of the circle towards the entrance of the marketplace. In the next part of the scene, the pillars are collapsing inwards towards the center of the circle and fall on each other before they crash on the pottery vendor.
When Hercules and Meg are talking after their day together, Meg is wearing a shawl. However, when she turns to talk to Pain and Panic disguised as birds in a nearby birdbath, her shawl is missing. It is there again when she is talking to Hercules.
After Meg and Hercules play hooky, they're walking down the stairs and Meg has a shawl around her. When Pain and Panic tell her to quit messing around she doesn't have it on. A few moments later it reappears.
Since this film is only an adaptation of the myths it is understandable for there to be quite a bit of artistic license taken with the stories. Any differences between this film and the myths belong in the trivia section of this site.
When Hercules spaces out after first meeting Meg, Phil yells "Earth to Herc!". However, the phrase "Earth to (insert name here)" was not coined until the first space shuttle launch. Since the movie takes place in ancient Greece, Phil should not have used this phrase but the inclusion of the line could easily be explained by saying that the intent was much like the water bottles that Hercules sells.