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.
When Maui's hook first appears on the back of Tamatoa's shell, the wrapping on the handle disappears briefly.
Near the end of the song "Where You Are", when Moana and her parents are walking to the temple, Moana looks to the right, and sees her grandmother dancing in the beach. (The shore runs parallel to the path). But when the song ends, the camera zoom out and the shore is clearly perpendicular to the path.
When Moana is a baby, her pet pig is a baby. Later on in the movie, Moana is all grown up, and the pig is still a baby.
When Moana meets the ocean with her grandmother, the ocean splashes her. Afterwards, she is immediately dry.
After Maui and Moana battle the Kakamora, he agrees to help Moana, and says they have to sail east. The sun is setting to his left, which would be west, so he is actually sailing north.
The movie features several frigate birds, particularly when baby Moana helps the baby turtle get to the sea. Polynesians sometimes used frigate birds to help navigate toward new islands. However, they spend very little time on land, and never eat there. They hunt while in flight in the open sea, and only land when they need to roost.
Maui says they must head east to reach Tamatoa's lair. But he spent the last 1000 years stranded on an island. How would he know which direction would take them to Tamatoa? As a master wayfinder Maui can navigate and determine location using stars, Sun, Moon, currents, and other methods. Indeed, he measured the stars just before determining that they had to go east.
In "Shiny", Tamatoa calls himself a "Decapod." He only has eight legs, including his pincers, while decapods have ten. However, in an earlier scene Maui mentions that he ripped off some of Tamatoa's legs.