Continuity mistake: In the scene where Bilbo, now invisible, sees Gandalf and the dwarfs run past the cave and he can't join them because Gollum blocks the way. When Bilbo finally runs past Gollum and kicks him in the face and knocks him down, the very next shot shows Gollum's body lying in the opposite direction, away from the direction Bilbo kicked him. (02:19:35)
Continuity mistake: As Thorin is picked up by the eagle, the eagle's talons roll him towards the camera. Both of the eagle's feet are in view and you can see all the way down Thorin's body to his boots. Orcrist is nowhere on his body during this initial shot of the pickup. As soon as the shot changes (where the Oakenshield drops free) and both of the eagle's feet come back into view, Orcrist is now on Thorin's body, running over his stomach and left leg. Had it been there before, it would have been visible when the eagle rolled him towards the camera.
Continuity mistake: Shortly after Bilbo finds the Elvish sword that turns blue in the presence of Orcs and Goblins there's a fight with Orcs at the entrance to the hidden valley. However, the sword doesn't glow blue. In subsequent fights with Goblins and Orcs the sword does glow blue, even when sheathed.
Continuity mistake: In the scene where Bilbo spares Gollum's life, Gollum turns around facing the invisible Bilbo and extends his right hand out to a rock. The far shots from in front of Gollum show his arm almost fully stretched out and his hand away. But the shots from behind Gollum show his right arm bent on the rock with his hand much closer and level with his head.
Continuity mistake: When the company are surrounded by Wargs outside the Hidden Pass, Thorin can be seen holding his sword Orcrist in one hand and an axe in the other; the shot changes and he is then holding his sword with two hands, the shot changes again and he reverts back to the original configuration. (01:20:25)
Continuity mistake: During the song "Blunt the Knives", Balin is seen in a shot from behind sitting at the end of the dining table. He is shortly afterwards seen dancing with a broom two doorways behind. The next shot then shows him sitting down again, bouncing plates off one he is holding. (00:27:20)
Continuity mistake: When Bilbo brings the two bowls of stew for Fili and Kili there's a spoon in each of the bowls, but after Bilbo sets down the bowls one of the spoons has vanished when he picks up the bowls again in the closeup, but the spoon reappears when they run after the Mountain Trolls.
Continuity mistake: In the scene with the mountain trolls, the captured ponies are in a corral untied. Over the course of the entire troll scene, the horses go from being free in the stall to being tied up by the reins.