Revealing mistake: When the hobbits ask Strider where he is taking them, he answers "Into the wild." A split second later as Strider walks past the camera the bow he carries on his back bumps into the camera, nudging the screen a bit.
Revealing mistake: After Sam dives between the Troll's legs and tries to crawl away, Aragorn and Boromir pull the chain that's around the Troll's neck to get him away from Sam. In the next two shots of Sam, his left wrist has an ace bandage wrapped around it - it's at his white shirt cuff. Notice the bar on his palm between his thumb and index finger. He did not have the bandage in earlier shots, nor does he have it in later shots.
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.
Revealing mistake: Once the secret door to Moria is open, when Gimli says, "Soon Master Elf, you will enjoy the fabled hospitality of the Dwarves," as Gandalf leads the way inside, note the glint of the trailing power cord as it moves along the ground behind Gandalf and goes directly under his robe. This is the staff's electrical supply cable.
Revealing mistake: While Boromir battles with the Uruk-hai at Amon Hen, to protect Merry and Pippin, there is a close-up of Pippin running towards an Uruk. In the first shot we see Pippin's face. In the next wide shot, not only are the two scale doubles noticeable, the back of the Uruk that Pippin is jumping onto, is also very different than in the next shot. The Uruk's back is much dirtier in this shot, and the clothes are different too.
Revealing mistake: When Boromir dies, Legolas and Gimli are standing nearby. This shot of Gimli's face and beard are very different here, because they changed Gimli's appearance after this. Most things were shot out of sequence. Compare his face in this shot to when they're fighting the Uruk-hai or when Gimli, Aragorn and Legolas are by the shore and decide to "hunt some Orc."
Revealing mistake: When Merry and Pippin run in on the Secret Council, you can see Elrond watch them come past him. However, for a few frames you can see that he keeps looking at where they came from even when they have gone past him. This is probably because they were superimposed on to the film.
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.
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.
Revealing mistake: When Gandalf is revealing Bilbo's ring as the One Ring to Frodo, he pulls Sam in through the window and onto a table. When it shows Gandalf looking at Sam, you can see that Sam's hand moves and is positioned in a rather odd way. This is because Sam in this shot is actually the rubber hand of a remote control dummy that they used instead of the actor. In the behind the scenes footage on the DVD you can see other shots of the dummy and Gandalf during this scene.