Continuity mistake: Just after Gandalf enters Bag End for the first time he looks the map of Middle Earth on the table. In first shot when he is grabbing the map, you can see that there are two scrolls and a flat empty paper stacked on the map. In next shot, there is only one scroll and a paper with some kind of pattern on it. (00:16:20)
Continuity mistake: When Gandalf says, "Mellon," the doors to Moria open and they all go in. Legolas soon picks up an arrow and says, "Goblins!" When he does so, we see the left long braid is loose at the end and coming undone. After Boromir shouts, "Legolas!" in the close-up we see the perfectly made long braid hanging down. (00:16:55)
Continuity mistake: In Bag End, as Gandalf goes towards the table with the map, the window bench to the left can be seen. On it lies a red blanket folded up up nicely. Later, when Bilbo is at the window looking out at the Sackville-Bagginses, the blanket isn't folded as it was before, and the book near the blanket has the papers on/near it arranged differently as well. (00:17:00)
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)
Revealing mistake: When Gandalf first visits Bilbo in Bag End they sit at a long table that is positioned lengthways from the camera. Bilbo potters about at the far end of the table and Gandalf goes to the left at the end closest to the camera. As he sits down the near half of the table wobbles but the far half does not. This seems to expose the fact that the table is actually in two parts, a small sized piece of table close to the camera next to which Gandalf looks large, and a normal sized piece of table a bit further away that looks the right size for Bilbo. The two pieces are filmed from such a perspective that they look like they join together in one long table and the fact that there is really a gap between them so that Bilbo is further away than it seems, makes him seem small compared to Gandalf. There is a round of cheese and various pieces of crockery on the near piece of table to disguise the gap. (00:17:10)
Continuity mistake: After Gandalf arrives at Bag End, in the wide shots looking through the doorway of the kitchen, the white cloth on the mantle over the fireplace hangs twice the length as it does in the next close-up, when Bilbo says, "I can make you some eggs if you'd-" Then, while they're in the kitchen, the white cloth hangs longer again. (00:17:20)
Continuity mistake: At Bag End, with his left hand Bilbo holds a plate with pieces of a sponge cake. The small part of the sponge cake is to the left of his thumb, and the large part is opposite his thumb. When there is knocking at the door, the smaller piece is to the right of his thumb. When he's at the window, the smaller piece is to the left again. As he runs into the kitchen, the large part of the sponge cake is now by his thumb. The plate never switched hands. (00:17:35)
Continuity mistake: The Watcher in the Water holds Frodo upside down, and just as its head comes out of the water, but before its mouth appears, in this shot part of the back of Frodo's cloak is tucked into his belt at the back of his waist. The cloak is not tucked into the belt in the previous or following shots. (00:17:45)
Revealing mistake: There is a shot of the Fellowship in Moria running towards camera as the entrance collapses behind them, in this shot you can see that the hobbits are obviously not Elijah, Sean etc. but their scale doubles. (00:18:15)
Continuity mistake: Gandalf and Bilbo sit on the bench outside of Bag End smoking and in the distance is the Party Tree, the tents and party lights, etc. from Bilbo's party. During the party, Bilbo is speaking with the lights above him and the position of various tents are shown during the entire celebration. Later, invisible Bilbo comes to the gate at Bag End and the Party Tree with all the tents surrounding it are seen (minus the tent that the rocket took and the tent that the 'dragon' burned). The position and arrangement of some tents, lights, etc. are different in all of these shots. (00:19:25)
Revealing mistake: Gandalf and Bilbo sit on the bench outside of Bag End smoking their pipes with the party area in the distance. The tree, the water, Hobbit home (future home of Sam and Rosie) to the right and party area is extremely different in dimensions and aspect ratio, compared to the background that's seen when invisible Bilbo comes through the gate at Bag End. It's also very apparent, because of the hair, that it's Bilbo's scale double in the back shots on the bench. (00:19:25 - 00:25:25)
Continuity mistake: When Bilbo and Gandalf are smoking pipes before the party, Bilbo makes a hoop with the smoke. The hoop first goes forward in west way position. But in the next shot the hoop is going directly forward in north way position. (00:19:25)
Visible crew/equipment: After starting their four day journey through the long dark of Moria, a few shots later Gandalf pulls on his hat brim, and just as he walks (with Legolas close behind) to his left (towards the viewer's right), up some stairs, the black electrical cable leading from the staff to under the robe's left sleeve is visible. (00:19:30)
Continuity mistake: At Bilbo's party, in the first shot Merry hoists Pippin up into the back of Gandalf's wagon. We see the arrangement of the assorted things in the back of the wagon. In the next front shot, as Pippin dives into the wagon we see a different arrangement of all those things in the back of the wagon. (00:21:20)
Continuity mistake: During Bilbo's party, in the first shot, as Merry boosts Pip onto the back of the wagon, on the table in front of the tent there are pears, oranges and apples on it. Once Pippin is in the wagon, seen behind Merry, there is one red apple that has appeared at the front of the table to the left of the other fruit that wasn't there before. (00:21:20)
Continuity mistake: At Bilbo's party, when Merry and Pippin set off the dragon firework, they are shown inside a small tent. The tent has dishes and other things in it, and is quite full. When the firework launches, taking the tent with it, you can see that all of the things inside the tent (with the exception of Merry and Pippin) have disappeared. (00:22:00)
Revealing mistake: At Bilbo's party, the rocket takes off with the tent. In the aerial shot, the ground below is seen and the ropes with the lanterns and streamers hanging from them are shown around the perimeter of the party. These ropes are suspended from wood posts staked into the ground. In the aerial shot all the ropes shown are arced and in a direct view from above we should not see an arc in all the ropes that are suspended on those posts. The aspect ratio of the lantern lights, shown to the sides of the streamer lines is skewed as well. The aerial view is CG. (00:22:55)
Continuity mistake: At Bilbo's party, as the fireworks dragon flies overhead, in the close-up shot, when Frodo calls out, "Bilbo!" the two people behind Frodo were not there in the wide shot just before this shot. This is not due to any Hobbits running. Also in that wide shot, Bilbo moves to Frodo's immediate left, but in that close-up he's away from Frodo, so Frodo has to move closer to him in this shot. (00:23:15)
Continuity mistake: When Bilbo is leaving, he drops the Ring at the doorway, turns and walks out the door. Gandalf steps outside after him. Gandalf never pulls at the door, nor does he even touch it. He stands outside talking with Bilbo. When the door is shown behind Gandalf it is wide open. Bilbo walks down the path with Gandalf looking at him. The next shot is a close-up and we see the shadow of the door opening to reveal the Ring. Then a shot looking up at Gandalf as he steps through the doorway. (00:23:40 - 00:24:30)
Continuity mistake: When Gimli falls onto his knees in front of Balin's Tomb in Moria, in one shot he's a few feet in front of it, in the next he is so close to it, that he could lay his head onto the tomb. In the following shot Gimli is further away again, so he should not have been able to reach it with his head. (00:24:20)
Answer: "Fly, you fools"