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: At the end, it shows Sam and Frodo walking through a forest. The very first shot of that scene shows Sam saying, "I wonder if we'll ever be put into songs or tales." In the background, through the trees, you can see the city of Osgiliath. Then it shows Frodo, with Sam in the background, and Frodo asks, "What?" In the next shot they are way further into the forest and you can not see Osgiliath. (01:44:40)
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: After Eomer gives Legolas, Aragorn and Gimli the horses and the Riders of Rohan are riding away, Arod (Legolas' horse) is being held by Legolas' right hand, but in the long shot, Arod is being held by Legolas' left hand and the horse is several feet to the left. (00:35:20)
Continuity mistake: Many times, when Gimli is seen with other people from a distance, it is clearly a smaller double which can be seen from the dark makeup around the eyes. This is especially noticeable when the shots are intercut with close-ups of Gimli. (00:37:55)
Continuity mistake: In Faramir's hideout behind the waterfall, Sam tells Frodo, "Use the Ring, Mr Frodo, just this once..." When the camera is on Frodo alone, the camera lighting shines on Frodo's right side, with his left in shadow. When the angle of the camera changes to show both he and Sam, Frodo's left side is then lit. (00:41:00)
Continuity mistake: At the battle of Helm's Deep, after the wall is breached we see the water flow out. Then there is an aerial shot of orcs entering the pool of water. It cuts to a closeup of Aragorn lying on the ground just in front of the pool, a very short distance from the orcs. He should have been visible in the aerial shot.
Continuity mistake: Very near the start, when Frodo and Sam are talking, keep an eye on Sam's backpack. The blanket rolled up at the top of it moves up and down his back, without him adjusting it. (00:06:10)
Continuity mistake: When Faramir and his Lieutenant are looking at the map, just after it's been unfolded, the Lieutenant puts his right hand out and points on the map with his right hand. In the following close-up, his left hand is doing the pointing on the map. All the close-up shots of the map were added later during pickups, to show more clearly where various characters are. (00:27:55)
Continuity mistake: When Sam, Frodo and Gollum are watching the Haradrim and Oliphaunts from the hill, the sun is shining on the left side of Frodo's face and on the right side of Gollum's face. In fact, throughout the sequence, the sun's position seems to change quite a bit, even though the scene only lasts a few seconds. (01:18:20)
Continuity mistake: When Gamling is fighting the Warg scout, after Hama's death, Legolas jumps off the high rocks, and starts running towards the Orc. There are high rock ridges behind and to the left of Legolas. As soon as the Orc scout falls to the ground, in the next shot of Legolas, as he runs toward the Orc, that background is flat and there is only one rock ridge directly behind Legolas. (00:09:00)
Continuity mistake: Gimli yells, "Aragorn!" then as he jumps into the air, on that same wall, is a dead body hanging over the edge, next to the smoldering lantern. In the earlier shot, just before Aragorn lifts his head down below, as the camera panned over the Deeping Wall, there was no dead body lying at the top near the edge, next to a smoldering lantern. (01:10:20)
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: In the extended edition of The Two Towers, during the 'Elvish Rope' scene near the beginning, the mist disappears and reappears between shots. When Frodo falls and lands at the bottom of the ravine, there is lots of thick, white mist swirling around, but when it cuts to a wider shot, it has nearly all disappeared within a second. In the next close-up shot of Frodo, it has reappeared again.
Continuity mistake: When the Warg Riders attack the people of Rohan en route to Helm's Deep, Aragorn falls off his horse with his sword in hand and it remains in his hand, however it is suddenly sheathed he prepares to grab a charging Warg.
Continuity mistake: When Gandalf, Legolas, Aragorn and Gimli step inside Meduseld (the scene where they arrive at Edoras in Rohan), as they are approaching Theoden the angle of Gandalf's staff changes. It appears from the shots taken at the front to be at an angle so that Wormtongue doesn't see he's still carrying it, but when cutting to the shots from behind the group his staff is almost vertical.
Continuity mistake: When Brego (Aragorn's horse) wakes up Aragorn by the river, after he had been thrown off the cliff, Brego is light brown. A few scenes later, Aragorn spots Saruman's army marching towards Helm's Deep, and in this shot Brego is all black.
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.