When Maui and Moana argue about whether or not she's a princess, Maui says, "If you wear a dress and have an animal sidekick, you're a princess." However, Moana is wearing a crop top and skirt, not a dress.
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.
In the beginning, Gramma Tala is telling the story in the gazebo. When Chief Tui knocks down the banners, the one to the left of the picture of Maui and to the right of Te Ka is a large monster but switches to a mountain and sea scene as baby Moana sneaks out of the tent.
When baby Moana picks up the first shell left by the ocean, she startles a fish who leaps back into the water and leaves a mark in the sand. In the next shot when Moana picks up the second shell, the mark has disappeared.
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.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
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.