After Anna's song, "The Next Right Thing," she stands up and put a bag over her shoulder. The strap of the bag lays over top of her hair, which is hanging loose. The "camera" spins around Anna, and when it returns, the strap is underneath her hair, making it appear as if the bag has gone through the hair.
When Elsa tells Yelena that something has called her to the forest, Anna is on Elsa's right side. But when it switches to the Fire Spirit's POV, Anna is on Elsa's left side.
Near the end of the movie where Anna approaches the guards protecting the dam, she tells them that her grandfather betrayed everyone. During that scene the female guard shield changes positions.
When Elsa, Anna, Kristoff, Sven and Olaf are approaching the forest covered with mist, they were close together. Then Kristoff, Sven and Olaf walk in a straight line to the mist but when the aerial shot shows, Kristoff, Sven and Olaf are further to the right.
The Arendelle soldiers have been trapped in the Enchanted Forest for "34 years, 5 month and 23 days" - in the wilderness and away from any production or services - yet their uniforms, weapons, and shields are in pristine new condition without any wear-and-tear, without any ability to repair or replace anything. Even assuming a magical slowing of aging (they all appear to have gray hair and such indicating they *have* indeed aged, they just seem youthful for how long it's been), usually such magic doesn't include protecting possessions from damage or day-to-day wear-and-tear, particularly as it appears these uniforms have been worn 24/7 during this time, or at least every day.
As Elsa's party is en route to the magic forest, there is a fleeting shot of her ice palace, which is still intact. But it's now summer and the ice palace is not at sufficiently high elevation to survive the warm temperature. It was possible to exist at that location only because of Elsa's magically-induced winter, which is now long over.
When Anna tells the Rock Giants to throw their boulders, the first one hits the middle of the bridge, but when Anna is running back to Kristoff and Mattias, that part of the dam is not broken.
Anna inciting the Rock Giants to throw their boulders was an incredibly stupid and hazardous way to remove the menace of the dam - when this could've been safely accomplished simply by partially opening the sluice gates, and then dismantling the dam once all the excess water had gently drained away. However, considering this occurred during the climax of the film, introducing real-world engineering methods would have been an incredibly dull letdown to the drama and action of the film, as well as losing the attention of its intended audience: children.
The Arendelle soldiers trapped in the mist doesn't make sense.
The youngest soldiers should be at least 18 years + "34 years, 5 month and 23 days" however they look 20 something. It is a common staple of fantasy that isolated paradise realms have atmospheres which cause people to age slowly.
When everyone is evacuating Arendelle, the wind is blowing everyone and everything in different directions but Elsa's hair doesn't seem affected at all.
Anna growls while acting out "villain" when playing Charades, but the whole point of the game is to portray the word or phrase silently.