When Willow gives Elora to Madmartigan, what is heard is, "Goodbye, little one," when originally, he said, "Goodbye, Elora." It was after the scene was shot that the people realized that Willow didn't know Elora's name at this point.
After Madmartigan rolls down the hill inside the giant snowball, a watchman shouts out that the soldiers are coming. Given how long and fast it took them to slide down, how did they get there so fast? Also, you hear clear clip-clop hoof-beat noises from the horses as they trample through loose powdery snow.
After the cart chase when Madmartigan and Willow get off the cart with the two back wheels missing, the rubber stunt wheel used to allow the cart to roll is visible in the center of the axle as it moves away from the actors.
Willow's hair is wet when he returns from the island. In a deleted scene, Willow was caught in a massive storm and went underwater. While we do not see this in the main movie, we can infer that it happened none the less.
Scratches inexplicably appear on Fin Raziel's face after the battle. In a deleted scene, her face was scratched up in the battle with Bavmorda. While we do not see this in the main movie, we can infer that it happened none the less.
During the fight in the castle at the end, Bavmorda's magic turns a clear day into an overcast storm. However, in a few brief shots of the sky during the fight between Madmartigen and General Kael, the sky is blue and clear with a few white clouds.