Continuity mistake: When Sam jumps at Frodo in Osgiliath when Frodo confronts the Nazgul, they both fall down some stairs. These stairs, seen from the top, have a wall to their left and are open to their right, where the camera is positioned. When they are falling down the first few steps, you can see their feet pointing towards the camera, in the next shot a few steps down it is their heads. (02:37:06)
Continuity mistake: When the Warg raises his head from his kill, he spots Gimli and he growls, showing his blood stained teeth. There are spikes on both sides of the harness around his neck. When he charges toward Gimli, Legolas kills him and he falls right in front of Gimli. There are no spikes on the harness, nor are his teeth stained with blood as before. (00:11:20)
Continuity mistake: When the Uruk-hai are being attacked by The Riders of Rohan you see Pippin on the floor with some mud on his face, yet in the next shot when he is almost crushed by a rearing horse he has got no mud on his face.
Continuity mistake: Aragorn, Legolas and Gimli fight the White Wizard who is standing on a rock. He overpowers them and when he says, "You are tracking the footsteps..." the backs of the three are shown. In this shot Aragorn stands to the right, closest to the rock with Gimli in the back to Aragorn's left and Legolas to the left of Gimli. In the very next front shot Aragorn is in the middle now, with Gimli standing near the rock. Legolas is standing in the same place. This has NOTHING to do with camera angle. (00:52:45)
Continuity mistake: As Legolas surfs down the steps, we see some dead bodies at the bottom of them, which he surfs right over. A few shots later, we see an aerial view of the wall with those same steps and there aren't any bodies at the bottom of the steps. (01:11:05)
Continuity mistake: When Gollum and Sam and Frodo are by the river and Sam and Frodo are talking about Gollum. Frodo turns around and yells something like, "What do you know about it?" When he yells this, he and Sam's faces are a few inches apart. When it cuts to both of them, they are about a foot apart.
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: Legolas says, "Look at them. They're frightened. I can see it in their eyes." In the next wide shot, we see Aragorn's back, men all around, and behind him, to the right, stands Dan Hennah, with wavy, grey hair, in his cameo. In the following close-up, we see Dan Hennah again, standing to Aragorn's left. We also see Alan Lee's cameo, whereas, in the wide shot, Alan's character is not there. (00:53:10)
Continuity mistake: At Henneth Annun, Faramir who is alone with Frodo and Sam, walks towards Frodo with his sword pointed at him. Behind Faramir, are many spears leaning against the wall. Then there's a shot of Frodo. In the very next shot there are fewer spears behind Faramir, and they are lined up very differently against the wall too. They are alone, and no one touched the spears. (00:41:50)
Continuity mistake: As Gamling and Hama ride past Aragorn and Éowyn, a snowy high mountain range can be seen right behind them. As they are riding past Legolas' view, over Legolas' head, another greener mountain range is right behind them. These shots were filmed at different locations. (00:08:15)
Continuity mistake: When Aragorn, Legolas and Gimli meet Gandalf the White in the Fangorn Forrest, Gandalf says that Hobbits whose tracks they are tracking "Have passed this way the day before yesterday." It cannot be so, because the day starts when Gimli says, "Three days' and nights' pursuit," Legolas says that blood has been spilled last night, and later Eomer confirms that they slaughtered the band of Uruk-hai during that night. Therefore, Hobbits could only have passed that way yesterday, more correctly during the night. Aragorn, Gimli and Legolas meet Gandalf immediately after they enter the forest, so it must be the same day (we know this because the forest is unknown to them; remember Aragorn telling Gimli to lower his axe). However, it fits in Gandalf's speech in Fangorn so beautifully, so it must be deliberate.
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: 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 Frodo and Sam are down below, near the Black Gate, wanting to run in, but Gollum is convincing Frodo not to, Frodo's pants have a couple of holes at the left knee. Later, when Gollum dives for the fish in the rocky stream, Frodo's pants don't have the holes at the left knee, as seen when he's walking with Sam. Frodo did not change his pants, and this is before they have spent the night, which is the scene right after this one. (01:06:00 - 01:36:55)
Continuity mistake: Just before Legolas surfs the shield down the stairs, he is holding the shield in his right hand and his bow in his left hand, which is down. In this shot, he starts to toss the shield down onto the ground, still clutching the bow in his left hand. In the next consecutive wide shot, the shield is still in mid-air, and as he is starting to run towards the moving shield, Legolas does not have the bow in his left hand now. He did not throw the bow over his shoulder. The next shot is a close-up of his feet on the shield, just starting to come to the stairs. In the next wide shot, as he is starting to surf at the top of the stairs, Legolas has the bow in his left hand again and he is lets loose the arrows at the Uruk-hai. (01:11:00)
Continuity mistake: When Aragorn is lying on the couch in Arwen's home, during the dream/flashback sequence, he at first has the edge of a grey/green pillow visible just above his right shoulder. After a cut to Arwen and then back to him again, the pillow has slipped down so that it cannot be seen behind his shoulder, though he hasn't moved yet. When he stands, the pillow can be seen on the couch.
Continuity mistake: When Theoden is mourning his son's death at his tomb, Gandalf is holding his staff to his left when shown from the back. When shown close-up from the front, however, he is holding his staff to his right. (01:04:20 - 01:05:55)
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: Faramir and his men, along with Frodo and Sam, are looking out towards Osgiliath, when someone says, "Osgiliath burns, Mordor has come." Originally, Minas Tirith is seen as well, as it should be, at the base of the mountains behind Osgiliath, which is geographically correct. However, Peter Jackson was forced by studio heads to edit it out of the theatrical version, because it was felt that seeing Minas Tirith then would confuse some viewers, who would think that Minas Tirith was Helm's Deep. In the extended DVD, much to the satisfaction of PJ, Minas Tirith was put back in order to be geographically correct. As heard on Commentary, extended DVD. (01:20:40)
Continuity mistake: When Merry and Pippin are at the Entmoot, in several of the front coverage shots, Merry is several feet in front of Pippin and slightly to the left. From the back at a distance, however, they are next to each other with Merry on the right. While there are some shots in which they are both moving around, accounting for the difference, here they are both stationary. Extended DVD, Disc 2. (01:11:50)
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.