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: At the Armory, in the first close-up of Aragorn, he looks at a sword in his hand and tosses it down. The right sleeve of his coat is ripped almost all the way around at the seam by his shoulder, and the sleeve is folded over where it's ripped. When he tosses the sword down, there is a glimpse of his left sleeve, and it too is ripped and folded over at the seam. In his next close-up, the right sleeve's seam is ripped much less and it isn't folded over. The left sleeve however, is ripped like in the earlier shot. This is not a case of shot flipping. (00:52:45)
Continuity mistake: When the three companions first meet Gandalf, after Aragorn drops his sword, Gimli lowers his axe and holds it by his right hand. When the shot changes, Gimli holds it by two hands and in a ready position. The same thing with Legolas, his bow changes position, and Aragorn with his legs. (00:52:50)
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: In the armory at Helm's Deep, Aragorn says in the close-up, "Then I shall die as one of them." As he turns and leaves, in the wide shot, most of the people that were near him in the close-up are not in this wide shot. (00:53:30)
Revealing mistake: Right after Gandalf gave warning that they would not be welcome at Rohan and jumped forward with his horse, next after him Legolas moved forward before Aragorn, you can see Gimli that rode with Legolas was a fake Gimli, the color of his skin was not normal, and he was too stiff. (00:53:45)
Continuity mistake: After Aragorn says to Haleth, "Give me your sword," in the wide shot we see that Aragorn is sitting on the tail of his coat and the coat is draped down the steps under his legs. When Aragorn rises, just after Haleth says, "...They say that it is hopeless," we see that the coat is not draped down the steps under his legs, as in the earlier shot. It is not the legs' shadow. (00:56:40)
Continuity mistake: After Hama says, "By order of Grima Wormtongue," we see Legolas handing a guard his bow, which he was carrying in his hand. Then in the front close-up of Legolas, we see him taking out the twin blades that are on his back and he even does the fancy spin with the blades in this shot. Then there is a shot of Gimli. Then in a side shot of Aragorn, Gandalf and Legolas, we see Legolas again taking out the twin blades that are on his back. (00:57:30)
Revealing mistake: The braids over Legolas' ears on his scalp, change drastically in position, shape, amount of hair that's braided and how it is braided, as does the amount of his side hair that is swept up into the back braid, in consecutive shots! The hair differs considerably in the following shots. In the armory, when Legolas and Aragorn argue and when Legolas apologizes to Aragorn, for despairing. When Legolas watches Aragorn hugging Haldir. When Legolas stands with Aragorn and Gimli on the Deeping Wall, awaiting the Uruk-hai. As Legolas lets loose the arrows towards the Berserker Uruk-hai. In these two shots too. First, standing outside of Fangorn with Aragorn and Gimli (flipped shot). Then, in Fangorn, saying, "This forest is old..."(flipped shot). (00:58:15 - 01:00:35)
Revealing mistake: At Helm's Deep, in the 1st close-up, Gimli says, "You could have picked a better spot," and two particular Elves stand at his left. In the next wide shot as Aragorn approaches, the Elves to the left of Gimli are different Elves than in the previous shot. One of those Elves from the 2nd shot is seen close-up when Aragorn walks away. Also, the second row of Elves is much closer to the first row of Elves in the 1st shot. (01:00:25)
Continuity mistake: When we first see Legolas on the wall with Gimli, Legolas is gripping his bow, left fist over right fist. Next shot as Aragorn walks over, his left hand grips the bow lower but his right hand is gripping the front of his quiver strap. Next shot, Aragorn is beside him, his left hand is much higher on the bow now. As Aragorn leaves, Legolas' left hand is lower on the bow again and his right hand is again gripping the front of his quiver strap. (01:00:25)
Continuity mistake: When Legolas, Gimli and Aragorn are standing atop the wall and Legolas says, "Your friends are with you Aragorn," in this close-up we can see that Legolas' right braid is loose and half undone. As Legolas lets loose his first arrow in the rain, his right braid is perfect again. Various close-ups were done in pickups long after the principal photography. (01:00:40 - 01:04:05)
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: In the two scenes, when Frodo and Sam are both up on the rocks and later, down below, hiding out of view, the Black Gate is in front of them. Earlier, is the view inside the gate. The two Trolls are pulling and pushing the wood 'pulley', to open the gate, while walking on the tall ramp that curves around. When the gate is open, that ramp should be in full view, from the angle that Frodo and Sam are positioned, but it is not. (01:03:55 - 01:05:55)
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 Sam, Frodo and Gollum arrive at the Black Gate, they hide at the top of the cliff looking down on the soldiers approaching Mordor. As the ground crumbles beneath Sam, the soldiers are some distance from the Gate's entrance, the shot switches as he falls then quickly resumes its original position. Yet the soldiers have now entered the Gate, all within the space of a split second. (01:04:30)
Other mistake: It seems as though the Elves at the battle of Helm's Deep aren't quite as coordinated and elegant as Elves are rumoured to be. During the Helm's Deep battle scene, Aragorn is shouting commands to the Elven archers. In the close up shot of Aragorn while it's still raining, look to the left of Aragorn, there is an Elf who gets hit in the head by the quivers on the back of the Elf next to him. (01:04:50)
Continuity mistake: In the scene where Frodo slides down the hill to get to Sam, when he reaches him, in this first shot, it is open ground, and very rocky around them. Frodo then conceals themselves under his cloak. When the two men are standing near them, looking around, the area behind Frodo and Sam is very steep, with a few large boulders right next to them. After Frodo lifts up his cloak, and starts to pull Sam's hand, the area is the same as in the first shot. AS he's pulling Sam's hand, the area and background around them, changes yet again, in this last close-up of them. (01:05:00)
Continuity mistake: Near the Black Gate, when two of the men from the marching army are walking towards Frodo and Sam, the decorative scarves at their necks change positions and are hanging differently, than when they turn and walk away from the 'rock'. It is not windblown. (01:05:05)
Revealing mistake: At the Battle of Helm's Deep, just after Aragorn slices the leg off the Uruk and just before Gimli slides down between the legs of another Uruk and smashes his axe into his chest, look carefully at the Elf on the left side of the screen. He arches his bow and fires, followed by a specific shooting bow sound effect, but there is no arrow. (01:05:30)
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.