Character mistake: When Maui and Moana set sail after defeating the Kakamora, Maui says they must head east. He turns the boat 90° as he says this. Throughout the next scene the setting sun is to the left of them (providing a beautiful backdrop to their fight), meaning that the boat must be heading north, not east.
Continuity mistake: After the chief stops his mother telling scary stories, pictures drop behind the kids. The one to the left of the one of Maui has three creatures with spiky heads. After the chief is knocked over we see those pictures again, and the one of three creatures has been replaced by one of an island with a cloud above it.
Continuity mistake: After Moana narrowly escapes drowning, she drags herself ashore next to some debris from a boat, one large piece especially, being by her right hand. After the pig runs away, she's not moved, but the debris around her has changed, and the large piece has disappeared.
Other mistake: In the beginning, when Maui is about to steal the heart of TeFeti, his back tattoos. On his right side, you get a glimpse of the tattoo of TeKa hitting him and him loosing his hook. He shouldn't have that tattoo since it hasn't happened yet.
Plot hole: All through the movie it is made known they have to get through TeKa to get to TaFiti. They fail and Maui leaves. Moana goes back alone and makes it through the barrier island and Maui returns to help her. The problem is he returns from the direction of TeFiti, if he can do that He could have done it all along, and therefore discovered TeFiti was gone.
Plot hole: Not knowing the twist at the end, Moana should have been overtaken by hopelessly knowing that Maui and a functioning fishhook are required to return the heart. We see right at the beginning that Maui was only able to reach the heart's resting place by transforming into a small lizard. The whole triumphant song is completely undermined as, based on available information she has 0% chance of success.