Continuity mistake: When Pippin says "What about second breakfast?" he's crouched over by the pony, a bit away from Merry. Aragorn says a line and the camera goes back to the Hobbits. Now Pippin is further from the pony standing right by Merry, not crouched at all. He couldn't have moved that far during Aragorn's line and be standing so naturally.
Continuity mistake: As Boromir and Aragorn talk right before Boromir dies, you can see Boromir's right hand gripping Aragorn's left shoulder in the shot from behind Aragorn's right shoulder, but when the camera view changes to Boromir's perspective, looking up at Aragorn, his hand is not there. The scene goes back and forth between these two views several times.
Continuity mistake: At the gap in the stairs in Moria, Boromir ducks as he is nearly hit by an arrow, and sheathes his sword. In the following close up he sheathes it again as he stands behind Gandalf.
Continuity mistake: When Boromir attacks him, Frodo frantically slips the Ring onto his middle finger (with the chain). Yet, as Frodo runs up the steps of the ruins, Boromir yells, "Frodo, I'm sorry!" and Frodo wears the Ring on his index finger. He is terrified, so as to remain invisible he does not change fingers.
Continuity mistake: As Sam, Merry and Pippin run across the grass towards the Bucklebury Ferry, they have two shadows; bold ones behind them, presumably meant to be from the moon, but also unexplained faint ones to their right. (This is before they pass the cottage, so it can't be light from the weak lamps hanging outside.) When Frodo is then pursued by the wraith his shadow is in front of him, yet he is running in the same direction as the other hobbits were.
Continuity mistake: Boromir gets hit by Lurtz's second arrow, drops down to his knees in front of Merry and Pippin, gathers strength, turns around and stabs an Uruk. In the next wide shot and close-up, he stands and is about to stab an Uruk in the back and the two arrows in his chest are there. Yet, in the next wide shot, as his blade is going down into the Uruk, Boromir has only the lower arrow in him, the one near his shoulder is NOT there, for 23 frames. In the next close-up, the upper arrow is back. These arrows are NOT CGI.
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.
Revealing mistake: When Frodo stops rolling down the snow covered hill, just before the shot of Boromir picking up the Ring, you can see the edge of the stockings that the actors wore to protect their feet since they were walking in real snow for that scene.
Continuity mistake: When the hobbits are hiding under the tree trunk from the Ringwraith in the beginning, you can see space to the left and right of the tree above them. Logically when the Ringwraith walks past the tree you would see it on the right side of the tree first, then on the left, but you don't - it looks like it walks out of the tree instead of behind it. [Confirmed on the commentaries - Elijah Wood asks his fellow actors if anyone spotted the mistake: 'It kind of magically comes out of the tree'. Sean Astin: 'You mean it doesn't pass from the other side?' Wood: 'No, it comes out from the centre.']
Continuity mistake: When the hobbits are sitting at the table in the Prancing Pony in Bree, Merry comes back with a pint. Pippin leaves to get one too. Then we see Sam mention to Frodo that a man is looking at them, across the table sits Pippin and no Merry.
Continuity mistake: When Frodo tells Sam about the Wood Elves, they both run up the hill and crouch behind a fallen log. In the shot of their backs and the elves in the background, Frodo is on the right side and Sam on the left. In the previous shot of their faces, Frodo was also on the right and Sam on the left. Extended DVD.
Revealing mistake: When Pippin falls in the Midgewater Marshes, you can see that part of his Hobbit foot is ripped off. Extended DVD.
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.
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: After the battle with the cave Troll, Aragorn rushes over to injured Frodo and brushes past some big rocks that wobble, showing that they are lightweight and not real.
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.
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.
Revealing mistake: When Arwen enters the water after being chased by the Ringwraiths, as she turns the horse, you can clearly see the fake hobbit (representing an injured Frodo), bounce up and down like a rubber band.
Continuity mistake: When the Fellowship meets in Rivendell, and Gimli tries to break the Ring with his axe, the axe breaks into many pieces on the platform upon which the Ring is laid. At first, the pieces are there in the close-up view. When the camera pans back for a long range view of the Fellowship, the pieces of the axe on the platform are gone. In the following close-up, the pieces magically reappear.