I went to see Moana on Thanksgiving and enjoyed it very much, even though I wasn't expecting it to be particularly good. One thing I was particularly delighted with was that Disney finally used something that wasn't straight European, Grimm or Andersen. I don't think they've used mythology since Hercules, either.
In some ways it felt like a return to the princess musical formula, and in others it was a departure. The animation was beautiful and realistic.
It was also, like their recent adaptations such as Tangled and The Princess and the Frog, more inspired by the tales than a straight retelling.
(Some of the following may be spoilers.)
They reference Maui being thrown into the ocean by his mother Taranga and raised by the gods, raising the islands from the sea, raising the sky, and catching the sun (which is very similar to other stories I've written about). The story of him stealing the heart from the island goddess is reminiscent of the Maori tale where he tries to steal immortality for humans from the goddess Hine-nui-te-pō and dies in the attempt.
They left out Maui's multiple brothers, whose number varies by version, but all of whom are also named Maui.
He was apparently a miraculous birth. He was born premature and unformed, or miscarried. Some sources say he was miscarried or aborted. The result is that his mother threw him into the ocean, but there the seaweed wrapped around him to save him. A god found him and raised him. Maui eventually returned to his mother, proved his identity, and his family accepted him. There are many different versions. Edward Tregear's Maori-Polynesian Comparative Dictionary lists quite a few of them.
Overall, I'd recommend this one. Disney's been making some good movies, but none of their films have wowed me like this for a while now.
This website is based on my research into folklore.