Continuity mistake: When Gollum is trying to catch the fish in the rocky bed of water, in the wide shot, Frodo and Sam are walking in the background. The background seen behind Sam and Frodo in that wide shot, is very different to the background in the very next shot, seen behind Frodo and Sam, when Sam says, "Hey stinker," and in the rest of the shots in this scene. The column in the wide shot is the same column seen behind Sam, when he says, "Because. Because that's what he is Mr. Frodo." There are three distinctly different columns shown in the close-ups! (01:36:50)
Continuity mistake: Sam helps Frodo up and says, "There's some good in this world," then Faramir walks over and the Hobbits face him. Sam's rolled blanket is seen high up on his back, above his shoulders. Yet in the very next close-up, which is a flipped shot, the blanket is way down on his back, way below his shoulders. Frodo's hair is completely different in both shots too. (01:36:55)
Continuity mistake: When Sam lifts Frodo and says, "That there's some good in this world Mr Frodo and it's worth fighting for", Sam's face is wet with tears and his eyes are red and teary. In the next shot, when Faramir walks over, Sam's eyes are still red and teary and his face is still wet, but in the next shot, when Faramir kneels, Sam's face is dry and his eyes are no longer red and teary. (01:36:55)
Continuity mistake: Just after Sam's speech in Osgiliath, the first shot of Faramir shows several men talking and eating, with a background of decorative stonework and a broken arch on Faramir's right. After the shot of Frodo and Sam, we see the shot of Faramir kneeling. Behind him, we now see different stonework and a squad of men charging forward as if to battle. In the next shot of Faramir, still kneeling, we see soldiers walking and milling around in front of the original background. (01:37:15)
Continuity mistake: When Aragorn first arrives in Helm's Deep and is confronted by Legolas, there are three close-up shots of Legolas saying, "Le abdollen" (you're late), "You look terrible," and then smiling. The bow visible behind his right shoulder appears to be his old Mirkwood bow. It is dark golden-brown, smooth, with a black bowstring. The one Galadriel gave him is the same color as his hair, elaborately carved, and has a light-colored bowstring. (for comparison check 1:43:20, where they are in the armory, and the bow should look even darker... but the white bowstring's visible there.) Continuity is screwed up as well, because in the shots between the close-ups of this conversation, where both Aragorn and Legolas are shown, the oddly-carved ends of his Lorien-bow are visible. (01:37:15)
Continuity mistake: At Osgiliath, when Frodo turns to face Faramir, just before Faramir kneels in front of the Hobbits, the Ring and chain hang outside Frodo's shirt. Yet just before Faramir says, "Then it is forfeit," the Ring is tucked inside Frodo's shirt. (01:37:20)
Continuity mistake: During Frodo and Sam's final scene in Osgiliath, you can clearly see that the chain Frodo is wearing has gotten much longer. In several shots while Frodo is on the ground, the chain hangs down below the shot, so you cannot see the Ring. (01:37:25)
Continuity mistake: When Faramir kneels in front of Sam and Frodo, in the close-up the hand of a Ranger is on Sam's shoulder. The hand and short fingernails are very dirty. After Faramir's lieutenant says, "You know the laws of our country..." the hand and longer fingernails are clean. Then in the next close-up the hand and short fingernails are dirty again. Sam's hood, hair, etc. differ in these shots too. (01:37:30)
Continuity mistake: In the first shot of the Uruk-hai running away fom Helm's Deep, towards the trees, the shot of Helm's Deep in the background is correct. The Causeway is littered with many bodies and the ladders are leaning against the Keep and the Deeping Wall with the break in it. However, in the next shot of them, as they are entering the forest of trees with Helm's Deep behind them, the Causeway has no bodies on it and there are no ladders leaning against the Keep. Also visible when Theoden is shouting, "Victory, we have victory." (01:38:00)
Continuity mistake: When Sam (in voice over) says, "But in the end, it's only a passing thing..." we see Gandalf's hair down and messy, during the battle. Just as Éomer is riding past Gandalf and the others, shouting, "Stay out of the forest!" notice Gandalf's hair in the side shot, it is neat, and pulled back. In the next close-up of Gandalf, looking at the Uruk-hai running into the forest, his hair is down again. (01:38:00)
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 Gandalf and the rest of the riders on horseback are watching the Uruk-hai retreating into the trees, in Gandalf's close-up, sitting directly behind Gandalf's horse is another rider on a horse. That rider has a silver helmet with the decorative high ridges in the center. However, right before that shot is shown, there is a wide shot of all their backs and a rider with that kind of helmet is not sitting directly behind Gandalf's horse, but rather further behind him, way off to his right. The close-up shot immediately followed the wide shot. Extended DVD. (01:38:20)
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: In the opening close-up shot of this scene just before Gollum says, "We wants it. We needs it. Must have the precious," Frodo and Sam are seen sleeping side by side. In the next wide shot of them they are sleeping perpendicular to each other. (01:38:35)
Continuity mistake: As this scene opens with an Uruk's body being dropped to the ground, the camera pans out to show Legolas and behind Gimli to his left, is a large rock. In the view from the front, now there is a dead Uruk sitting up against the same rock, where there was none before. He's dead, so he didn't move there between shots. Extended DVD. (01:38:50 - 01:42:55)
Continuity mistake: The bodies and rocks behind Gimli change positions, between shots. When Gimli says the words, "That's not bad for a pointy-eared Elvish Princeling," there is a rock right behind Gimli to his right. In his close-up it's not there. Yet, when the camera does another close-up, when he reacts to the arrow between his legs, the rock is to his right again. When Gimli says the words, "I myself am sitting pretty on forty three," behind him to his right, a Rohan turns over the body of an Uruk onto its back. When Gimli says the words, "He was already dead," that Uruk hasn't been turned over. (01:39:00)
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: In this shot, Pippin grabs some apples and a green ear of corn, then he puts it all into his left hand, starts to turn around and with his empty right hand he reaches for a floating cauliflower. The camera angle changes, and in the next shot, we see him holding an apple and corn in the right hand and another apple in his left hand. Floating to the right of him is no longer a cauliflower, but a green bottle. Extended DVD. (01:40:05)
Continuity mistake: At the end of the film, when the heroes of the big battle are watching the lightning over Mordor, while Gandalf says the words, "The battle for Helm's Deep is over", over Legolas' right shoulder is a far view of the Deeping Wall and the Causeway. There is no break in the wall, or ladders at the wall, nor are there any bodies anywhere on the Causeway or otherwise. (01:40:13)
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)
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.