Revealing mistake: After Bilbo returns from the party invisible and finds Gandalf by the fireplace, look at Gandalf as Bilbo walks between him and the fire. There is no shadow cast on him when there clearly should be. Also as the camera pans round following Bilbo's movements, you can see Gandalf is casting a shadow on the floor but not on the table, but when Bilbo walks up to it he does, even though Gandalf is between him and the fire light. (00:25:10)
Continuity mistake: After Sam dives between the Troll's legs and tries to crawl away, in the first shot the Troll lifts his leg and in the second shot he's about to step on Sam, who is in the middle of the floor. Yet in the very next shot Sam is already at the wall raising his left arm and wincing at the giant foot coming down on him. (00:29:50)
Audio problem: When Bilbo and Frodo are reunited at Rivendell, Bilbo embraces Frodo and Bilbo's voice can be heard saying "Oh." But, his mouth is closed and could not have possibly said it.
Continuity mistake: The Fellowship hide when they spot Crebain from Dunland. In the wide shot when Aragorn picks up his stuff, Frodo runs and lying on the ground under the rocks in front of him are blankets, coats, etc. Then in the next close-up under the rock, the position of those things lying on the ground is different just before Frodo dives onto them to hide. (00:06:40)
Continuity mistake: Extended Version only: When the Sackville-Bagginses are knocking on the door, Bilbo walks to a beam to look at them through the window. In the shot from behind we see that he walks to it and leans his right arm on it, peeking round. From the front he's leaning his whole shoulder on it, looking more relaxed. (00:17:00)
Continuity mistake: When the hobbits first start to run away from Farmer Maggot, they are running through the corn, which is much taller than them. Two seconds later, when the camera angle changes to the wide view (you can see all four hobbits running through the corn), their heads are even with, if not slightly above the corn. After it shows that the corn is about their height, there is the last shot of them coming out of the corn field and the stalks are again much taller than them. (00:50:20)
Continuity mistake: There's a close-up of Frodo's face after the camera shows the stone Trolls, and Frodo's face is shining with sweat. Then Sam says, "Look Frodo, it's Mr. Bilbo's Trolls," and there's a shot farther away from Frodo's face. In this shot, Frodo's face has no signs of sweat on it. Extended DvD. (01:14:40)
Continuity mistake: When the invisible Bilbo returns to Bag End he chats with Gandalf, then leaves dropping the Ring on the floor near the door. In the first shot of it after he's left, the Ring is touching a crack in the tile. When he gets closer, the Ring's moved away from it. (00:28:50)
Audio problem: When Haldir is seen talking to the Fellowship in Lothlorien in the extended edition, he says "You can go no further." From Aragorn's point of view you can see Haldir saying "You can go no-" but when Haldir is walking away, he isn't moving his mouth to say the word "further." (00:46:18)
Continuity mistake: When Lurtz was about to kill Boromir, Aragorn knocked the Uruk-hai down. He falls, drops his bow and arrow, then he picks up a sword and shield off a dead Uruk. Once Aragorn and Lurtz start fighting, the dead bodies disappear. When the fight is over and Lurtz is dead, all the dead reappear. (02:40:43)
Continuity mistake: At the beginning, when Gandalf first knocks on the door at Bag End, Bilbo runs out and hugs Gandalf, with both arms around Gandalf's neck. In the shots behind Gandalf, both of Bilbo's arms are around Gandalf. In the shot behind Bilbo, only his left arm is around Gandalf. (00:15:55)
Continuity mistake: When Arwen and Aragorn are talking on the bridge, she caresses his cheek and forehead. In the next shot, her hand is no longer on his face.
Continuity mistake: When Gandalf knocks on the door at Bag End, there is a small uneven path of stones mingled with grass in front of the door, where Gandalf stands. Once Gandalf and Bilbo enter Bag End, in the interior shot that area is visible past the front door, and now it is an even stone path with no grass whatsoever between the stones. (00:15:30)
Continuity mistake: In the scene at the Council of Elrond, in Rivendell, after Frodo has placed the Ring on the stone table, the council argues about who will take the Ring. Just a moment before Gandalf does that touching look towards Frodo, he starts yelling at Boromir. His posture and action in the wider angle shot do not match that close-up moment. Extended edition. (01:43:25)
Continuity mistake: There is a scene where Merry is throwing rocks into the water in front of the Walls of Moria. The camera shows him starting to throw a second rock into the water, and then the shot cuts faraway to show the rock landing in the water. In this brief faraway shot, Pippin is sitting. In the very next shot, however, Pippin is standing, poised and ready with a rock in his hand. (00:14:52)
Continuity mistake: Near the end when Frodo has tears running down his face. In the first shot the tear on his right side is short and the left side tear is down to his chin. in the next shot they are reversed. Some people have said it's just that one tear lengthened and a new one started, but look at the right-hand one (the longer one in the first shot). If there was a new tear, we'd still see the damp path of the first one, but it's rolling down a dry cheek. (01:25:45)
Continuity mistake: In the Chamber of Mazarbul, with Balin's Tomb, Pippin backs up towards the well, we see the pail and there is a thick bunch of chain hanging out of it. In the next shot of Pippin as he backs up and turns, the pail now has one line of chain hanging out of it. Then Pippin touches the quiver of the arrow, and in the first shot of the head falling back into the well the pail yet again has a thick bunch of chain hanging out of it. Then in the next shot of Pippin turning around towards Gandalf the pail once again has the one line of chain hanging out of it. (00:26:45)
Audio problem: When Bilbo is saying good-bye to Gandalf outside, he's standing by the door and then he turns to walk to his gate. When the camera angles behind Gandalf, Bilbo is standing at the gate with it open; the gate is too far away for Bilbo to have been there in a split second, and we never hear the gate open, but we hear it squeak shut. (00:29:15)
Continuity mistake: In the establishing shot of Gandalf and Frodo riding along in the horse-drawn cart, Frodo reaches the brim of Gandalf's hat. Yet when it goes in for the closeup, either Gandalf has grown a foot or Frodo has shrunk. (00:11:40)
Continuity mistake: This mistake is at the end of the film, when the Orcs are walking outside Saruman's tower going to catch the Hobbits. The colour of the sky changes between grey and blue. (02:20:00 - 02:21:00)
Answer: "Fly, you fools"