Character error
When Maui and Moana argue about whether or not she's a princess, Maui says, "If you wear a dress and you have an animal sidekick, you're a princess." However, in this scene, Moana isn't wearing a dress. She's wearing a crop top and skirt.
Continuity
Before the song "How Far I'll Go," Sina finds Moana sitting on a tree throwing sticks into the ground. However, when Moana begins to sing, the sticks are no longer there.
After washing up on Maui's Island, Moana's body and hair are covered in sand. She gets up and walks towards the water as if to wash the sand off her body. She is distracted by the approach of Maui and she hides behind her boat, never washing off the sand. From this scene on, the sand has disappeared from her body and hair, not a grain on her, even though she never cleaned it off.