Revealing mistake: In Emyn Muil, just after Frodo says, You will lead us to the Black Gate," Sam and Frodo are following after Gollum. You see Frodo, with Sam trailing, come around a large rock formation from the left of the screen, then Frodo passes a large round boulder on his right and starts to run down a slope towards the camera. As Sam passes the same large boulder on his right, you can see it shake from him brushing against it. (00:13:40)
Continuity mistake: After the sweeping pan of Edoras, Gandalf, Legolas, Gimli and Aragorn ride up towards the Golden Hall. In the first shot, behind them is a wood fence with a wood ladder, leading up to a tower and seen behind Legolas are two girls standing on stone steps. Also seen in this first shot, to Gandalf's right, is a man with a white beard, hooded shirt and long vest. In the very next shot, is the same bearded man (use zoom) wearing the same clothes, standing near a cart. In the next shot, the first close-up of Aragorn, to his left, are a woman (partially seen) and two men wearing hats, standing under a wooden structure. Aragorn looks up at the Golden Hall, and sees Éowyn. The next shot of Aragorn, behind him to his left, are the same wood fence, ladder, tower and two girls on the stone steps, as in the first shot of them all. As they continue to ride up, Gimli remarks, "You'll find more cheer in a graveyard." Just after Aragorn looks up at the Golden Hall again, in the next close-up of Aragorn, to his left, are the same woman and two men standing under the same wood structure, as in the first close-up of Aragorn!! (01:16:25)
Continuity mistake: After Aragorn says to Haleth, "Give me your sword," in the wide shot we see that Aragorn is sitting on the tail of his coat and the coat is draped down the steps under his legs. When Aragorn rises, just after Haleth says, "...They say that it is hopeless," we see that the coat is not draped down the steps under his legs, as in the earlier shot. It is not the legs' shadow. (00:56:40)
Continuity mistake: When Aragorn fights with the Orc riding the Warg, Aragorn knocks the Orc off and he falls to the ground. Then the Warg tumbles off the cliff with Aragorn. If you notice, the Orc falls a fair distance from the cliff, but when Legolas and Gimli ask him what happened, he is much closer to the cliff edge. (00:12:45 - 00:13:40)
Continuity mistake: Throughout the movie, the size of Gimli changes several times. Upon entering Edoras, his height is just under Legolas' shoulder. When the Uruk-hai attack Helm's Deep and they are waiting atop the wall, you can hardly see Gimli's helmet, but all of the other characters (for example Legolas) stand there behind the wall that reaches the height of their kidney-area. (01:18:00)
Deliberate mistake: Legolas leaps onto Arod and as he rides, both of his hands are clean. After they've just clashed into the Warg riders, in the close-up of Legolas as he releases his arrow there are dark smudges visible on Legolas' fingers and knuckles on his right hand. In the close-up of Legolas as he lets loose the arrow into the Warg that is about to attack Gimli, we see both of his hands are smudge free. This shot is flipped, so the right hand that was previously smudged is now the left hand, which is clean anyway. (00:11:00)
Continuity mistake: At night at the Dead Marshes when Frodo is lying down he is holding the Ring in his hand and he's stroking the Ring with his middle finger. In the very next close-up he's stroking the Ring with his index finger then in the next wide shot he's stroking the Ring with his middle finger again. (00:47:25)
Continuity mistake: On the way to Helm's Deep, when they stop for the night, Éowyn offers Aragorn some stew. As Aragorn is putting the spoon into his mouth, in the wide shot, there is a piece of 'white food' hanging over the side of the bowl near his right hand, Aragorn's hair is messy, blowing on his forehead and his hair is put behind his left ear. In the following close-up shot of his reaction to the taste of the stew, the 'white food' isn't hanging off the side of the bowl, his hair isn't as messy on his forehead and he has more hair in front of his ear now. (00:01:40)
Continuity mistake: At Helm's Deep, in this opening wide shot, soldiers call out, "Come on, keep moving. Quickly now," as the people walk towards the Glittering Caves. We see the soldiers standing up against the wall, as the people go past. Next, in a side close-up, Aragorn talks with Legolas as they walk past the soldiers, and other people. In the next shot from the front, as the conversation continues, they're still walking past the guards and people. In the second and third shots the people around them differ and in all three shots the guards differ too. (00:50:45)
Continuity mistake: Elves, as can be seen all through the battle of Helm's Deep, carry their sword and arrows on their backs, protruding some distance above their shoulders. When the elves arrive at Helm's Deep, however - none of them appear to be carrying a sword (it is possible that the sword could be sheathed at the waist, under their robes, but it seems unlikely that they'd change it to a back-sheath later on), nor do they have any arrows for the bows that they are carrying. (02:04:25)
Revealing mistake: At Helm's Deep, Theoden says, "I want every man and strong lad..." behind them is Gimli, who has a conspicuously reddish face, and his beard is split down the middle into two braids. Éowyn confronts Aragorn, she apologizes and hurries off, walking between Legolas and Gimli, who looks the same as in the earlier shot. It's obviously Brett (scale double) in both shots, the beard with its two thin braids are completely different when next we see Gimli, in a close-up at the armory. This time the beard is full, with hair between the two very thick braids, and his face is a normal color. (00:51:50 - 00:52:55)
Continuity mistake: Merry and Pippin run into Fangorn Forest and drop down on the ground. First there is a wide shot of Pippin falling, then there's a close-up of them, and last there's an extreme wide shot of the area. The area that Merry and Pippin are lying in is different in all three shots. (00:38:15)
Continuity mistake: When Aragorn dreams of Arwen, he lies on this couch with Arwen leaning above him. She caresses his cheek down to his jaw. Then the camera angle changes and her hand is near his hair. (01:19:56)
Audio problem: On the Deeping Wall, Theoden says, "Draw all our forces behind the wall..." but Theoden's lips are moving before we hear him say those words. (00:17:10)
Continuity mistake: The first two shots of people leaving Edoras are shown, and in the wide shot Éothain and Freda are seen on their horse, as well as the people in front and in back of them. Next are shots of Theoden and Gamling speaking, and the Aragorn and Éowyn confrontation. Then in the next shots the people are still seen leaving Edoras, including Éothain and Freda with the same people in front and in back of them as was seen in the much earlier shot! (01:33:50 - 01:35:50)
Revealing mistake: The very first shot of the Uruk-hai running through the rock canyon is the exact same shot that is shown in the last shot of this scene, just after Pippin bites the Lorien brooch off his cloak. Even though in between those two shots, all the Uruk-hai have been running until they meet up with the Orcs. In between those two shots, the rock formation shown behind the Uruk who lifts his fist up is also quite different in the next successive shot, when the Orcs approach the Uruks. (00:14:40 - 00:16:50)
Continuity mistake: When Sam, Frodo and Gollum arrive at the Black Gate, they hide at the top of the cliff looking down on the soldiers approaching Mordor. As the ground crumbles beneath Sam, the soldiers are some distance from the Gate's entrance, the shot switches as he falls then quickly resumes its original position. Yet the soldiers have now entered the Gate, all within the space of a split second. (01:04:30)
Revealing mistake: Éomer yells, "To the King!" at Helm's Deep and the Rohirrim begin to ride down, towards the Uruk-hai. In the very first wide shot of Gandalf, starting to lead them down, there is a clear reflection of three of the riders and their horses, shown on the ground. (01:29:55)
Audio problem: When Gandalf rides off to find Eomer, Shadowfax isn't wearing any sort of harness. But just as Gandalf rides out of the stable past Legolas, you can hear a jingle, like a bridle would make. (01:30:20)
Continuity mistake: After riding down the Causeway at Helm's Deep, Aragorn looks up and sees Gandalf. In the first shot his hair and face are very sweaty and shiny. In the second shot when he says, "Gandalf," his face is dry and sweat free. His hair is different in both shots too. The second shot was pinched from the earlier scene in the Keep when he looks up at the window remembering Gandalf's words, "Look to my coming." Confirmed on commentary. (01:29:25)
Answer: The movie makes it clear that Gandalf has lost some of his memory and his personality has changed. Gandalf actually did die and pass over to the "other side", as it were but was sent back to complete his task. However, he was sent back as a similar, but different entity. Gandalf the White does not have all the memories of Gandalf the Grey, at least at first. He doesn't even remember that he used to be called Gandalf the Grey until someone points this out to him. It is implied that Gandalf doesn't even remember Sam until Aragorn mentions him. Gandalf then searches his memories and remembers who Sam is and his eventual importance to Frodo's quest. When he finally remembers this, he is pleased that Sam went with Frodo, as he will play a crucial role near the end of the journey.