Genius Bonus: In Ancient Greece, bards would typically recite epic poems orally. At the beginning of epic poems, the bard would usually request that a muse sing for him in order to tell a more "accurate" story. Examples of such a request is seen at the beginnings of The Iliad and The Odyssey; muses were considered the true speakers of the tale and the bard just the mouthpiece. At the beginning of Hercules the narrator is interrupted by the muses who proceed to sing the tale in his place.
The changing of the Titans' beings doesn't make much sense at first; until you look at them as the stages that the Earth went through before civilization popped up.
The thunderstorm during Hercules' battle with the Hydra seems really random and conveniently thematic; then you remember that Zeus controls thunder and lightning, which means he must be watching from 'upstairs' and is worried for Herc's safety.
The prophecy told by the Fates was that, "should Hercules fight," Hades would fail. When Pain and Panic are interrupted while they're poisoning Hercules as a baby, Hercules fights them off and survives - Hades' fate had already been decided in the first few minutes of the movie!
For all the changes they made, Disney kept all of Herc's central character traits— Hair-Trigger Temper, impulsive nature, tendency to devote himself utterly—and they're what drives the plot in the end.
A Running Gag in the animated movie is that Phil always says more or less words than he counts. The first instance of this: "Two words! I am retired!" Except in Greek, it is two words (Είμαι συνταξιούχος).
When does Hercules bring Meg back to life? Only after he becomes a God. Herc resurrecting her was a miracle that could only be accomplished by a divine being, which he had just become.
As the main page points out, there is an apparent plot hole between the animated series and the movie, due to Hades being surprised to learn the Hercules is alive in movie despite having antagonized him throughout his teen years. However, there is a way to reconcile these two. In classical cartoon bad guy fashion, many of Hades plans to kill Herc in the series involve placing him in peril remotely, and just assuming that the plan worked and that he is dead, only for the hero to show up to foil him later. Indeed, it is exactly this type of behavior that leads to his reaction in the movie. So, its possible to suppose that at the time that Hercules interrupted Meg's deal with Nessus in the movie, Hades was still under the assumption that Herc was dead due to a much more recent death plan he had sent Pain and Panic to enact on his behalf (and which they again bungled and lied about, since they clearly never learn).
During the song 'I won't say I'm in love', there is a line 'That's ancient history, been there, done that!' But ancient history is the period the movie is set in! It implies she's not entirely over what happened yet.
A common subject of Greek comedies were parodies of classic myths and one particular sub-genre known as satyr plays would insert drunken satyr shenanigans into the story to create humor or conflict. This is possibly why they chose to portray Phil as a comical nymph-chasing satyr instead of the human he originally was.
The Fates' Prophecy - "Should Hercules fight, you will fail". Consider how Hercules ends up saving Mt Olympus in the first place; he's desperate to prove himself worthy of being a God, he's gone through all the Hero training necessary for such a task, he's motivated to stop Hades for revenge, he wants to hurry it up so he can save Meg etc. If he hadn't been depowered, it's likely he might not have been able to save Olympus. Hercules would have been the most obvious threat to the Titans so they might have done careful planning so he was quickly neutralised. And Hades would have had the element of surprise as well. In the film he wasn't expecting Hercules at all and the Titans were unprepared. So the Fates set Hades out on a Self-Fulfilling Prophecy.
Besides Nessus' assault on Meg, she's probably been forced into similar situations to help Hades make deals before...
We're never told just how long Meg's been working for Hades. She could have been his slave for decades or even centuries, since he controls her soul, including whether or not it can pass to the Underworld.
When watching Disney's Hercules as a child, it looks like that centaur-monster was just hassling Meg, right? But try watching the same scene with a better knowledge of the mythology, listen closely to the dialogue, and... squick. Yeah, he's trying to rape her. And just to add more horror on top of that... he's not only half horse, he's half giant horse.
Oh, and if you also know the mythology, you know that in the end, when Hercules is married (though not to Megaera), that same centaur (Nessus) winds up killing Hercules with a poison shirt in revenge for an incident like this one.
For that matter, the reason Hercules isn't married to Megaera when he is killed with the poison shirt is because he went mad and killed her and their children (it's why he had to do the twelve labors).
And in the original mythology, Hera hated Hercules because he was not her biological child and was responsible for much of the hardships of his life.
Actually, it was more that; he was named after her - his Greek name was really Heracles, and Hercules was his name in Roman. But Hera was later grateful to Heracles when he saved her from being raped by a giant.