Continuity mistake: In the scene just after the Riders of Rohan give horses to Aragorn, Gimli and Legolas, you see them riding away. Two riders at the back of the group are riding white horses. Yet in the next shot, there are only riders on black horses at the back of the group. (00:35:20)
Continuity mistake: When Legolas and another Elf are dragging Gimli back to the Keep, in the front view the Elf's quiver is empty. Yet in the next shot from behind, the Elf has many arrows in the quiver on his back. The arrows would be seen from the front, because they are way above his shoulder in the back shot. (01:13:40)
Continuity mistake: In the extended DVD, when Gimli quips, "That's not bad for a pointy-eared Elvish princeling!" the back shot of Legolas shows him 'toying' with his bow, but in the front shot, his hands are apart holding the bow. (01:39:00)
Continuity mistake: At the Dead Marshes after Gollum rescues Frodo, in the next opening shot while Sam sleeps we see the pot and pans lying on the ground near Sam's head. When he hears the Nazgul he wakes up and some of those things lying near his head earlier are not there in this shot. This has nothing to do with camera angle. (00:47:15)
Continuity mistake: On the way to the old sewer in Osgiliath, in the first shot, we see Faramir leading Frodo and Sam with Gollum in the rear. In the next two shots, Gollum is directly behind Faramir now, with the two Hobbits reaching the entrance first. Extended DVD. (01:41:35)
Continuity mistake: In Osgiliath, before Sam's speech, in the wide shot showing Sam's back, the large fry pan hangs down, below the small fry pan, on Sam's back. In the next shot, in front of Sam, the large fry pan is seen sticking out, just behind Sam's right shoulder. (01:35:10)
Continuity mistake: When we first see Legolas on the wall with Gimli, Legolas is gripping his bow, left fist over right fist. Next shot as Aragorn walks over, his left hand grips the bow lower but his right hand is gripping the front of his quiver strap. Next shot, Aragorn is beside him, his left hand is much higher on the bow now. As Aragorn leaves, Legolas' left hand is lower on the bow again and his right hand is again gripping the front of his quiver strap. (01:00:25)
Continuity mistake: Just before the trees start killing the Uruk-hai, we see the backs of Gandalf and the rest of the heroes on horseback as they're watching the forest. Gandalf is holding his staff up in his right hand. Next close-up shot, he's lowering the staff in his left hand. Extended DVD. (01:38:20)
Continuity mistake: When Frodo is pulled out of the swamp by Gollum, Frodo's hair is dripping wet, then not as wet in the next shot, then his hair is matted on his forehead and then off his face. (00:46:55)
Continuity mistake: In the extended DVD, right before Faramir lets Frodo, Sam, and Gollum go, he grabs Gollum around the neck. The problem is, he grabs Gollum from behind, so his hand is on the back of Gollum's neck. He then pushes Gollum up against the wall, but suddenly his hand is in the front. I've watched this closely, and there isn't enough time for Faramir to twist his hand around. (01:42:20)
Continuity mistake: At the flooded Isengard, the first shots of Pip and Merry are in front of Saruman's storeroom. Floating in the water, directly behind them are a large barrel and a large crate. In the shots of them turning to enter the storeroom, the floating barrel and crate are gone. Extended DVD. (01:40:15)
Continuity mistake: Just as Éomer rides past Gandalf, Aragorn and the rest of the riders that are on horseback, Éomer yells, "Stay out of the forest!" and when he yells, "Keep away from the trees!" on the left of the screen, he and his horse have turned around and are now pointing towards Gandalf and Aragorn. In the very next shot, a close-up, he is facing the opposite way and is just then turning his horse around, to face out, towards the Uruk-hai running into the forest. (01:38:05)
Continuity mistake: When Frodo and Sam are eating the Lembas, the camera angle switches back and forth between them. At one angle, the Ring once again is first outside, and then at the next shot of him, it is back inside the coat. (00:07:15)
Continuity mistake: As Theoden draws his sword before the cavalry charge from the hall, there is a rider to the right of Legolas at the edge of the screen. When it changes to a wider shot, the horse and rider are no longer there, and there is a clear space where they were standing. (02:31:48)
Continuity mistake: At Edoras, standing on the steps of the Golden Hall, Hama says, "I can not allow you before Theoden King so armed...By order of Grima Wormtongue." Then Gandalf, Aragorn, Legolas and Gimli disarm themselves and give their weapons to the guards. After requesting not to be parted from his 'walking stick', the next wide shot shows them walking towards the door, with the guards at the sides holding the weapons of the four visitors. Yet in the very next shot from behind, though it still shows them walking towards the door, the guards at the sides changed their positions, note the ornate columns. For example, in the first shot, to the right of Aragorn standing near the steps, is the guard holding Aragorn's sword, bow and arrows. In the second shot from behind, that guard is now on the other side of the column, closer to the door on Aragorn's right, standing next to another guard, who's holding Gandalf's sword and Legolas' bow. (01:17:40)
Continuity mistake: In the scene where Frodo slides down the hill to get to Sam, when he reaches him, in this first shot, it is open ground, and very rocky around them. Frodo then conceals themselves under his cloak. When the two men are standing near them, looking around, the area behind Frodo and Sam is very steep, with a few large boulders right next to them. After Frodo lifts up his cloak, and starts to pull Sam's hand, the area is the same as in the first shot. AS he's pulling Sam's hand, the area and background around them, changes yet again, in this last close-up of them. (01:05:00)
Continuity mistake: In Osgiliath, after Frodo and Sam fall down the steps, Frodo is sitting on top of Sam holding Sting to his throat. In the wide shot, Sam's leg is beside the wall. Yet, in the close-up, when he starts to rise, the wall is right next to his head. (01:34:20)
Continuity mistake: Just after Eomer removes his helmut in the close-up shot, in the wide shot of the group, look closely at Eomer's mouth. You can see it is moving as if he was talking, but in that shot, there is no dialogue. (00:33:30)
Continuity mistake: When Sam first reaches into his pack, in the close-up, he takes out the lembas bread and says, "Oh yes. Lovely", one corner of the leaf is sticking up. As he continues to say, "Lembas bread", in this wide shot, all the corners of the leaf are now down and completely covering the lembas bread. (00:07:20)
Continuity mistake: When the Uruk-hai are on the causeway, after using the battering ram on the door. The shape of the opening in the door varies between the outside shots and indoor shots. (01:16:40)
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.