These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Some of the gods in the TV series have gotten a fan following, especially Aphrodite.
Thalia, the short, fat muse, is pretty much everyone's favorite. Fittingly, Thalia is the Muse of comedy - even in the original myths.
Evil Is Cool: Hades, though anyone with magical powers and the voice of James Woods would be cool.
Fan Dumb: There were actually Christians out there who were shocked when they let their kids watch this movie and then found out it "glorified Greek mythology." Though why you would let your kids watch any film without screening it first yourself if you're that controlling about what your kids are exposed to... (And never-minding the fact that this "Greek" mythology was presented using values that were generally judged to be more "Christian" in nature. And the Muses are singing gospel!)
Genius Bonus: Many, for the Greek mythology buffs in the audience. "Zero to Hero" is full of half-second allusions to Hercules' Labors, famous Greek (and Roman) art, as well as ancient Greek culture.
When the kids are stuck under a rock, they shout, "Somebody call IX-I-I!" Technically wrong (Seeing as this is Greek, not Roman) but if you know your numerals, you know they're saying "Call 9-1-1!"
Greeks Hate Hercules: While the rest of the world's audiences and critics liked the movie well enough (though, of course, not to the extent of The Lion King and the earlier Renaissance films), The Greeks despised this movie, even denying the film a premiere in Greece. Then again, the decision is justified, as the Greeks didn't care much for the many glaring mistakes to their own mythology, even if the rest of the movie was pretty decent. It's kind of similar to how a lot of American historians hated Pocahontas (even though that didn't get banned; it just got slammed with a lot of criticism) while other countries liked it well enough.
Memetic Sex Goddess: Megara, who would make girls who wound up interested in girls look back on moments this may have been incredibly evident in the past (like the moment she appeared on screen and also did her washing-hair-in-the-river-thing), and boys do much the same, likely earlier, possibly whilst swallowing the same way Herc does.
Squick: The first time we meet Megara is while she is being sexually assaulted by the enormous centaur, Nessus. And this ain't one of your happy, frolickingFantasia centaurs.
This becomes even worse to people familiar enough with Greek mythology to recognize the name Nessus. Nessus was a centaur killed by Hercules who tricked his wife into using Nessus's blood to create a poisoned tunic that caused Hercules to die a horrible, painful death.
Some fans make pair of videos on YouTube where he sings The Land of The Dead by Voltaire which actually fits him perfectly.
According to the DVD commentary for the first Family Guy episode he starred in, James Woods hates to sing. Additionally, even though he loves playing Hades, Rob Paulsen voiced his verse for the House of MouseVillain Song "It's Our House Now".
Ahem. 'Hercules and the River Styx'. James Woods singing 'My Town'. 
Since when do Disney characters use the same voices singing?
What an Idiot: Hades sent his monsters to deal with Hercules instead of challenging him to a fight, which means he would easily defeat the latter with his godlike powers. What was he expecting?
There are a number of signs that the gods have limits on the degree to which they can interact or interfere with mortals. For example, Zeus and Hera never even visit Hercules' foster parents to explain who and what he is, and Zeus only communicates with Hercules by animating his statue in his temple, even after he first meets with him, so he's not just waiting for Herc to make first contact. If Hades has to do all his work indirectly, or through catspaws, it explains his lack of direct action.
Also, he was secretly planning a takeover of Olympus, so a direct confrontation would be a bit too obvious (not that Hades is anywhere near subtle, but still...)
Hades gets Hercules to agree to give up his strength for 24 hours while he releases the Titans to take over Olympus. Then he decides to send the Cyclops to kill Hercules for no good reason. This ignoring that sending a giant to out will likely lead to Megera getting hurt, therefore breaking the deal and Hercules getting his strength back, plus, he ignores that the Fates said ''Should Hercules fight, you will fail", his strength was NEVER stated to be a requirement for him for Hades to fail.
Base Breaker: Icarus. Some fans see him as a crazily awesome, hilarious and occasionally wise character. Others see him as childish and grating.
Crosses the Line Twice: In the episode about Prometheus, rather than dancing around the fact that his liver got eaten by an eagle every day, the writers went out of their way to make every possible reference to it. However, the scene where the eagle visibly pulls his liver out, and then they proceed to argue about the eagle seasoning it while he's eating it, takes the cake.
Hilarious in Hindsight: Idina Menzel made a guest appearance as Circe, a singing witch. Later, she would go on to play Elphaba, who just so happens to be a singing witch.
And again in Disney's Frozen, where Idina Menzel plays, you guessed it, a singing Witch (sort of)
Relationship Sue: Played with; Hercules tried to make one out of clay. It failed; When it was time to create her personality, Aphrodite interpreted "Crazy about Hercules" as a Clingy Jealous Girl. It doesn't take her long before she invoke Ax-Crazy as well. When he tries to fix her personality by making her a "independent woman", she instantly put him in the friendzone. To make it worse his crafting skills were so bad, that Aphrodite had to parody the Sims just to make her look human.