Revealing mistake: After Haldir dies, Aragorn jumps onto the only ladder resting against the steps 'inside' the Deeping Wall. Hanging onto the ladder, he then falls on top of the Uruk-hai down below. The ladder is now lying on the ground perpendicular to the steps of the wall. However, when Aragorn runs up the stone steps on the side of the Keep, in the aerial CG shot of the wall below, the ladder is not lying on the ground where it should be, under the scurrying feet of the Uruk-hai. (01:14:35)
Continuity mistake: Merry wakes up to find Pippin drinking the Ent water. During this scene, Merry's cloak changes, to either with or without leaves on it and the amount and position of the leaves vary too. (01:08:15 - 01:10:00)
Continuity mistake: At Henneth Annun, Frodo and Sam have their blindfolds removed, and to their left are two barrels. In the 1st shot, one barrel has a brown cloth draped on it with a bowl of nuts and cracked shells and on the second barrel, candles that are not lit. In the 2nd shot, Faramir walks in and to his right the brown cloth under the bowl of nuts is draped differently, the candles, which are lit now, are a different variety and there are also ceramic jugs near the barrels now. After Frodo answers, "Yes. For my part," Faramir gets up and as he walks, the items on the barrels look the same as in the first shot. (00:29:00)
Continuity mistake: While running in Fangorn Forest, Aragorn stops kneels down and then says, "These are strange tracks." In the wide shot preceding just as he kneels down, and in the close-up when he says those words, his position and the position of the rocks and trees surrounding him are very different in both shots. This has nothing to do with camera angle. (00:50:55)
Continuity mistake: Aragorn, Legolas, Gimli, Theoden and others are in the Keep after the walls have been breached, while Aragorn is talking to Theoden about riding out together and the like, Legolas and Gimli are tipping tables up and putting them against the door. However, in one shot when Aragorn is asking about a passage to get the women and children out look behind him, Legolas and Gimli are standing with their weapons drawn, then in the next shot they're back to tipping tables up.
Continuity mistake: What happened to Aragorn's wounds on his shoulders after his fight with the Wargs? When he talks to Theoden on the outer walls of Helm's Deep, the blood is pretty much gone, only the fabric is stained. Later, when he and Legolas have their little heated discussion about the defenders of Helm's Deep, the blood is back again on the skin. (01:55:00)
Continuity mistake: During Theodred's funeral, as the bearers of the body lower Theodred off their shoulders, there's a close-up of the soles of Theodred's shoes. As Éowyn starts singing, the body's being passed towards the tomb. There's now another close-up of the soles of Theodred's shoes. The marks on the soles, of the right shoe in particular, are quite different in both shots. The helmet doesn't block the view of the soles on the shoes in either shot. (01:24:45)
Deliberate mistake: On the Wall of the Hornburg, in the close-up of Aragorn, he dramatically draws his sword with his left gloved hand. In the next close-up of Aragorn, when he yells, "Hold!" he raises his left hand with the ring on his index finger. In editing, they wanted to have the Elves on the left of the screen and Uruk-hai on the right, so they flipped the first shot. (01:02:45)
Revealing mistake: As the Uruk-hai are slamming into the chamber door, with the battering ram, Gimli and Legolas are standing at the door. Across the room, Aragorn says, "Ride out with me," then in the next three shots of Theoden, he's standing in front of the same wall, with particular markings. In the very next shot, Gimli says, "The sun is rising," and he's standing right in front of the very same wall that Theoden is standing right in front of. Then, in the next shot, still standing at that wall, Theoden says, "Yes. Yes. The Horn of Helm Hammerhand..." Both Theoden and Gimli, can not be in front of the same wall at the same time. In the next shot of Gimli, still standing at that same wall, responds, "Yes." He then starts to go off to blow the Horn. The next shot, is a close-up of the door - all the men in front of it and some wood are knocked away, due to the force of the battering ram. In the next shot, as Theoden says, "Let this be the hour when we draw swords..." between Aragorn and Theoden, the men are seen huddled together at the door again, and Legolas and Gimli are there too. Yet, in the next shot, Gimli is hurriedly running up the steps of the tower to the Horn. (01:27:20)
Continuity mistake: After the shot of Gandalf, Aragorn, Legolas and Gimli riding towards Edoras, there's a close-up of Theodred. In this shot there is a red pillow next to Theodred's face on his right. In the wide shot behind Éowyn, there is no red pillow to the right of his face. Though there is in this shot a white pillow corner leaning on the headboard, that is not in the previous front wide shot. The fur cover at the foot of the bed lies differently in the front and back wide shots too. (01:13:35)
Continuity mistake: After the tree has buried Merry and Pippin in its roots, the close-up of those roots (gnarled and twisted) do not look anything like the roots of the tree in the far shot (straight and broad), when Treebeard says, "Away with you, you should not be waking." Not a case of distance - in the wide shot when Treebeard arrives, just after they're let go, you can compare that shot to the shot just before, and the roots are very different, regardless of the Hobbits' size. (01:10:45)
Continuity mistake: Just after Treebeard stomps on Grishnakh, with his left leg, he leans forward on that left leg, then Pippin yells, "Run Merry!" Then we see in the side shot that Treebeard now picks up his right leg and starts to move it forward. Then mid-step, in the next front shot, we see that Treebeard is now putting his left foot down, not his right. This has nothing to do with camera angles. (00:39:35)
Continuity mistake: As the Uruk-hai charge the walls of Helm's Deep, the elves release their arrows first, no problem here. However, when the Rohirrim shoot, the arrows that strike the enemy are not the short, brown-leather fletched arrows that they should be using, but the long white-fletched elven arrows.
Continuity mistake: During the scene when Frodo, Sam, and Gollum are in the Dead Marshes, Gollum begins saying, "Once it takes hold of us..." Gollum moves closer to Frodo as he reaches for the Ring, and then Frodo slaps his hand away as he says, "Don't touch me." You can tell that Gollum was very close to Frodo, however, in the next shot, after Frodo bats him away, Gollum is much farther away than he could possibly be. (00:44:20)
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: 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.
Deliberate mistake: During the Warg attack, Aragorn is being dragged by the Warg and is heading for the cliff. In the very last wide shot of Aragorn, from behind his head, we see the hillside and riders behind the Warg, where they just came from. Next, we see a couple of shots of Gimli finishing off a Warg. In the next wide shot, the hillside including riders and bodies is the same one as earlier, only it's been flipped. (00:12:50)
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)
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.