Continuity mistake: The flower that Theoden is holding while he is in front of his son's tomb has 8 petals, but when he drops it, it has only 6, and the flowers on the ground have only 5 petals. (01:25:30)
Continuity mistake: When King Theoden, Aragorn, Gimli and what's left of the army are trying to stop the Uruk-hai from breaking in, Aragorn says, "Tell the women and children to head for the mountain pass.." and pushes Gamling toward the back entrance, so Gamling is in front of him. Then Theoden says his line about so much death and the next shot shows Aragorn and Gamling turning their heads. Now, Aragorn is closer to the back entrance than Gamling. (01:27:05)
Continuity mistake: Aragorn remembers what Gandalf said, "...at dawn look to the East." Theoden crosses the floor in front of Aragorn saying, "The horn of Helm Hammerhand shall sound in the Deep," as Aragorn turns around towards Theoden. Theoden now turns to face Aragorn, as he continues, "one last time." In the next shot, Theoden puts his hand on Aragorn's shoulder, behind Aragorn is a chair to his right. The next shot of Theoden close up shows his back to the front guarded door of the chamber with the chair overturned behind him. Earlier when Theoden crosses the floor past Aragorn, their positions changed. It should be Aragorn's back facing the front guarded door of the chamber now. Also, the overturned chair should be upright. (01:27:20)
Continuity mistake: At Edoras, as Éowyn says, "Now the Wildmen are moving through the Westfold, burning as they go, rick, cot and tree," Aragorn and Gimli sit at a table across the room. In this shot, the candle on their table has drippings going down the side of the candle. When Aragorn says, "You have two thousand good men..." the candle is taller and does not have those drippings. Aragorn says, "Open war is upon you..." and the candle now has more drippings than in that first shot. (01:27:35)
Continuity mistake: When the Uruk-hai slam into the chamber door with the battering ram, just before Theoden yells, "Forth Eorlingas!" we can see the damage done to the wood on the right door on the outside. As the Uruks start to run in, we also see some different damage to the metal trim on that door. However, as Theoden rides past that door on his horse, the damage to the door is gone! (01:28:35)
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)
Continuity mistake: The Evenstar on Aragorn's neck moves from side to side during the scene with Gandalf in the stable, before the evacuation of Edoras and also at Helm's Deep when Aragorn is talking to Theoden on the walls. (01:29:30)
Continuity mistake: In the shot where you see Gandalf, Eomer and the Rohirrim riders appearing in the East, you can see that the Uruk-hai's shadow is pointing towards Gandalf, i.e. towards the direction the sun is supposedly coming from.(From the viewpoint of Gandalf and Rohirrim, as they ride down the hill towards the Uruk-hai.) (01:30:15)
Continuity mistake: In the opening shot of the stable scene, there is a saddle in the stall next to Brego. A few shots later, you see a man lifting that saddle and start to walk away. There is no saddle in the next few shots. Then the saddle is back again, for Éowyn to pick up. (Extended DVD.) (01:30:35 - 01:31:40)
Continuity mistake: In the stable, just as Aragorn takes Brego's lead rope from the Rohan, in the shot of Brego moving backward, the two knots at his halter are seen. In the next shot as Aragorn continues soothing Brego he moves in closer, the two knots seen differ from the previous shot and there is no excess rope on Brego's left knot. However as Aragorn unties the knot on Brego's right, the excess rope of his left knot is seen, which differs from the second shot. (01:31:00)
Continuity mistake: In the stable at Edoras, Éowyn gives the saddle to someone, then starts to walk towards Aragorn, and her long hair is spread out all around her shoulders. Cut to the close-up shot, and her hair is now parted at the neck, hanging straight down in front and back. When Aragorn walks away, her hair is all around her shoulders again. (01:31:40)
Continuity mistake: At the destruction of Isengard, the dam is broken and the river is starting to break through the wall. In the wide shot as the river starts to break through, we see the wall breaking and all the CG Orcs at the top of the wall falling. In the next close-up, we see the CG Orcs still standing on top of the wall and when they do fall in this close-up, they fall very differently than in the previous wide shot. (01:31:55)
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)
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: At Osgiliath, when Frodo first brings Sting to Sam's throat, in the first close-up the chain is not caught up on the vest button. When Frodo falls back and drops Sting, the Ring's chain is hooked up on the button. The shot changes to Sam then quickly back to Frodo, and Frodo says, "I can't do this Sam" and the chain is no longer hung up on the button. (01:34:50)
Continuity mistake: In Osgiliath, when Sam says, "I know. It's all wrong. By rights we shouldn't even be here," he is standing up right next to the wall. In the next shot, of Sam's back, he is standing a few feet away from the wall. In the next shot, he's next to the wall, and then starts to walk to the archway, for his 'Sam' speach. (01:34:55)
Continuity mistake: After Aragorn asks, "What do you fear my lady?" in the following shots the hair at her shoulders changes position between the front of her shoulder and behind her shoulder, in the different camera angles. (01:35:00)
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: Gollum's hands are bound behind his back, during Sam's speech. After Sam's speech, Faramir walks over and while he's speaking to Frodo and Sam, Gollum is shown rubbing his hands. Faramir has not yet said, "Then it is forfeit. Release them." Gollum's ties would not yet have been cut. As explained on the commentary, they needed shots of Gollum for this sequence, so they pinched them from other moments, and inserted them here. (01:35:15 - 01:37:45)
Continuity mistake: When Saruman is telling the Orc to send out his Warg riders, in the close-up, Saruman lets his staff hit the ground and then in the shot of his back, his staff goes down again and it is in the opposite hand. (01:36:40)
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.