When Gandalf rides out, using the light of his staff to ward off the fell beasts so Faramir's team can get back to Minas Tirith, you see that Pippin is on the horse with him, even though there would have been no reason to bring him along. The reason is that this scene was originally filmed to coincide with Gandalf and Pippin's arrival at Minas Tirith, but was pushed further back as the story evolved.
The Orc commander orders the archers to "fire" their arrows. This sense of the word originated when fire was used to ignite explosive weapons, e.g., to discharge artillery or firearm, and was extended later to discharge of any missile, e.g., arrow.
Prior to Faramir's ride to re-capture Osgiliath, Gandalf challenges him. There is one shot where Faramir comments on the "Men of Gondor" there are a number of words before this phrase but his lips do not appear to moving.
After Frodo wakes up in Minas Tirith, Merry and Pippin stand in the doorway. Their height reaches the middle of the ornate door carving in the close-up, but in their next wide shot running in, they are considerably lower. When Legolas and Aragorn walk in, also in a close-up, their height is just a bit higher on the carving than the two Hobbits' heights were. Then when Sam stands in the doorway his height also reaches the center of the carving.
When at the Black Gate, the army of men are surrounded by Orcs, then after Aragorn's "For Frodo" line, they charge across the screen from left to right. When they are running, in a shot where Gandalf is seen on the very right of the screen, you can see through some gaps and there are no Orcs, just an open field.
After Gollum says, "Clever Hobbits, to climb so high!", he jumps onto Frodo and Sam. Gollum then attacks Frodo and when he turns Frodo onto his back, Frodo's shirt is wide open at his neck/chest and the chain and Ring are gone. In the next close-up as Gollum chokes Frodo, and the following shots, the chain with the Ring is back.
When Gandalf and Pippin are in Minas Tirith, and Gandalf is outside he starts coughing on his pipe smoke. On this wide shot, Pippin is tucked into bed. Then, in the next shot, he is up standing by his bed looking at his new Gondorian armor. He then gets Gandalf some water from the pitcher.
When Gollum drops the lembas from the bridge, you see the leaves it was wrapped in falling away, and the wafers fall generally straight down. However, when Sam finds it later, the lembas is still mostly wrapped in the leaves, with only a few morsels broken off and laying around unwrapped.
Before the charge of the Rohirrim, we see that Merry and Eowyn are near the middle of the group, but when we see Merry during the charge, look behind him. There are about five horsemen, behind whom are just empty fields.
When Aragorn's party rides to the Black Gate, Eomer is shown as riding with them (he can be identified by the white plume on his helmet). When they reach the gate, Eomer is missing from most of the wide shots, although he's shown in at least one close-up.
When Sam rescues Frodo in the tower, as he puts the ring back around his neck, you can clearly see the scar from the stab wound on his right shoulder. However, in "Fellowship", he was stabbed in the left shoulder.
While Denethor is eating in the citadel hall and is asking Pippin if he knows how to sing, he has a smear of red wine/sauce/blood on his chin. In a subsequent shot, Denethor turns to the camera and the smear is gone. It then reappears as he looks back to Pippin.
When Eowyn pulls off her helmet to kill the Witch King her hair is fairly neat. In the next shot as she is crawling away and calling for Merry, her hair is very messy. Then when she is leaning over Theoden, her hair is neat again.
When Gandalf and Pippin conclude their meeting with Denethor and leave, the bottom of Gandalf's robe clearly has been soaked in dirty water. Then the next shot of his robe from behind shows it to be clean.
In the ride of the Captains of the West and the army from Minas Tirith to the Black gate, Aragorn's hair is suddenly - and obviously - a different wig. The hair is longer, straighter, and the hairline is different. While it's conceivable that Aragorn might have cleaned up a little bit before he took charge of his new kingdom's army, his hair couldn't have grown that much, and his hairline shouldn't have changed.
When Frodo and Sam are bewildered as the orc army marches out from the fortress by the bottom of the secret stair, they are lit from the bridge's direction by red and orange fiery colors. In the reverse shots of the bridge and the fortress, there is no orange light in the shot at all, only the ghostly green lighting.
Sam rolls down Shelob's back, then he grabs Sting and takes a stance against Shelob. In the next wide shot, Sam stands ready and Shelob positions herself at the stairway. Frodo's wrapped body is not lying anywhere to be seen.
When Aragorn first meets the Army of the Dead, he is holding a torch in his left hand and a sword in his right hand. When he turns around to look at the rest of the undead, his torch and sword have switched hands. He then turns around again and the torch and sword are back where they originally were.
When Theoden "reforms the line" as the Mumakil approach, there are empty fields behind the horses. In the overhead shot of them charging, it is seen that there are still orcs in the background who should have been there in the previous shot.
When Pippin is recovering from looking into the Palantir, the shots alternate between Gandalf and Pippin. In the shots of Pippin, you can see Gandalf's hand holding the side of Pippin's face. In the shots of Gandalf, the hand is no longer there.
When Frodo is panicking and stuck to the web in Shelob's lair, shortly before he pulls out Galadirel's Phial, his Elven cloak sticks to the web and is pulled off of his shoulders. Yet, in the next shot of him (Galadriel's voice-over) it is still on his shoulders.
In Minas Tirith, when Gandalf swings Pippin up behind him on Shadowfax and they ride up to try to save Faramir, Gandalf has his staff in his right hand. When they arrive at the Tomb of the Stewards, the staff is gone and Gandalf has take a spear from one of the soldiers at the door to use as a weapon in attacking Denethor.
Right after Éowyn and Merry saying "to battle", there's a scene where a trebuchet is throwing a fiery rock into Minas Tirith. You can clearly see that the rock won't fly for more then a dozen feet or so, thus there's no way it made it over the walls of Minas Tirith like seen in the next shot, unless the trebuchet stood right at them.
When Gollum throws the Lembas bread over the cliff, we see it breaking apart, the wind blowing the parts away. However, when Sam finds the bread again, the pieces are all rather neatly assembled at the foot of the cliff.
Just before the army of Rohan begins its ride to Gondor, Theoden tells Merry he cannot come along. Merry is standing in front of his horse. A few moments later, Eowyn picks up Merry. Merry's horse is gone.
The two doors of the Black Gate continue to open as Aragorn and the others ride away from the approaching Orc army. When Aragorn rides as he shouts, "Sons of Gondor, of Rohan, my brothers... when the age of men comes crashing down," at the top of the screen the "closed gate" is visible.
Denethor prepares to eat as he goads Faramir into attacking the orcs. Faramir leaves the hall. There should be a time delay as Faramir puts on his armor and organizes the attack. Yet while Pippin signs and the attack begins Denethor is still eating this meal.
When Aragorn is running back to join his fellow men, when the black gate is open, we can see the CGI flag of the rider that goes with him is going from left to right, but in the next shot, the wind is in the opposite direction.
When the camera pans over the tower of Isengard where Saruman is being held captive, you can see the entire top surface - and that he is alone. A few moments later, Grima appears behind him - also imprisoned at the top.
After Pippin draws his sword, the next shot is of Orcs running to the right of the screen. As that shot opens, click five or six frames in and two crewmembers are seen between the Orcs on the right of the screen, click a few more times and more crew members are visible in the middle, between the Orcs.
In the scene where Frodo and Sam encounter and fight with Gollum on the slopes leading to Mount Doom, Frodo starts running towards the entrance to the Crack of Doom. Not only are they on top of an erupting volcano, but they are also in Mordor, which as both the books and films would have us believe, is a arid, barren, and totally dry location. However, as Frodo runs up the hill, there is clearly trickling water in the background, indicating a large stream.
The troll attempting to break the door down while Gandalf talks about death is using a blacksmith's plate forming hammer. Not a weapon of war, these are used for forming bar stock into sheets. The plate forming hammer is common in many of the book illustrations, especially concerning the dwarves.
In theatrical cut, when Pippin informs Gandalf that Denethor is about to burn Faramir alive Gandalf has his staff in his right hand. But when they arrive at the Tomb of the Stewards, the staff is gone and Gandalf has take a spear from one of the soldiers at the door to use as a weapon in attacking Denethor. This is considered a continuity error. But in fact, there is a scene in between which is cut from theatrical release but restored in special edition in which Gandalf's staff is broken by the Witch King during their encounter.
There is no stairway or other form of entry to the roof of Orthanc. This is most evident in the extended edition of ROTK: Grima's sudden appearance behind Saruman when moments before an all revealing overhead shot didn't show him or any means for him to get there.
When Faramir tells Gandalf and Pippin he has seen Frodo "not two days" earlier, Gandalf and Pippin have been riding for at least three days from Rohan to reach Minas Tirith, not counting the day before at Rohan and the day they spent at Minas. According to the "The Two Towers", Faramir met with Frodo and Sam before all this happened, so at least 4 days earlier, maybe 5 days.
Orlando Bloom's eyes are brown, but as Legolas, his eyes are changed to blue using CGI. In close-up outside the Black Gates, his eyes are CGI blue, but in a shot immediately following with Gandalf in the foreground and Legolas in the near background, his eyes are clearly brown.
After Gorbag says, "You touch it, and I'll stick this blade in your gut", Shagrat and Gorbag start to fight. A few shots later there's a close-up of Gorbag being bald - he's not wearing his hairpiece/wig in this shot-as he's being pushed towards the right of the screen by Shagrat, just before falling into the hole! (On the Extended Edition DVD Director/Writer commentary, writer Philippa Boyens actually admits that his wig falls off!)
At the beginning of the film, Gandalf confronts Saruman at Orthanc. Saruman is standing on the top-most platform of Orthanc 500 feet above the ground, while Gandalf and his party are standing very close to the bottom of the tower. It is clear from the elevated camera angles that those on the ground would have to be looking almost straight up to be able to see Saruman, and Saruman would have to be leaning out over the edge looking nearly straight down to be able to see those on the ground. Thus the entire scene is logistically impossible as depicted. The actors on the ground are not looking up nearly high enough to see Saruman, and when Legolas shoots his bow he is not aiming high enough to reach the top of the tower. Saruman is not close enough to the edge to even be visible from the base of the tower, and Wormtongue is even further back than Saruman, yet he is somehow shot by Legolas from below. Finally, it would not be possible for them to hear and speak to one another at that distance. It would be like standing on top of a 50 story building (Orthanc is 500 feet tall) casually talking to someone on the ground. That is why in the book, Saruman and Wormtongue speak to Gandalf from a window above the entrance, instead of from the top of the tower.
In the scene where Gandalf and Pippin are racing through Minis Tirith (when they first arrive to talk to Denethor), in one of the shots where Shadowfax is turning a corner, you can see that the Pippin on his back is in fact a dummy.
When Legolas jumps on the back of the elephant, he goes to cut the rope to release the people. However, there are about three thick rows of ropes going through the back of the elephant. Legolas only cuts one. The other ones were already cut.
In the scenes when Pippin is lying in his couch in Meduseld, tormented by the urge to watch again the Palantir, next to him there's a Rohir sleeping. While when Pip stands up to go to Gandalf the proportions between the hobbit and the man are right, in the scene before, when he's helplessly trying to sleep (before the scene in main hall between Aragorn and Eowyn), Pippin looks about as high as the Rohir.
Right before Legolas jumps onto the Oliphant, he is counting kills as he shoots arrows from his quiver. As he is counting, however, he clearly is not pulling any arrows out of his quiver. He is just faking the motion.
When Aragorn speaks to Legolas and Gimli before they enter the Path of the Death, you can see a green shimmer in the back showing the King of the Death, exactly in this moment a knight of Rohan crosses between Aragorn and the entrance, but the shimmer which is supposed to be several yards behind him appears "over" him.
When Smegol/Gollom is plotting the hobbits' demise by talking to his reflection in the river he coughs and dribbles. As his face is directly above his reflection the spit should drop directly onto it but it drops 'downward' as if he were upright.
Near the beginning, after a toast, Aragorn tilts his mug up to drink from it, and the shadow from the liquid inside is clearly visible through the translucent bottom indicating it's made from plastic and not some kind of metal as it's made to look like.
After the negotiations with the Mouth of Sauron (Extended DVD version), Aragorn decapitates the Mouth of Sauron. The Black Gates open, and the Orcs march out, but as the camera pulls back to a wide angle shot showing Aragorn and the others ride back to their army, there is no sign of the Mouth's body, or of his horse.
During the early stages of the Battle of Pelennor Fields (at Minas Tirith), the two sides use massive trebuchets against one another, loaded up with large stones and fiery projectiles. However, later in the battle, when the Rohirrim arrive, and later when the oliphaunts [sic] and army of the dead do battle, these large blocks have disappeared from the battlefield. Several towers in the city of Minas Tirith which we see smashed during the early fighting, also appear to be intact later on.
At the end, when the four Hobbits are entering Grey Havens,
Sam is wearing a yellow vest with brown buttons over a white shirt. When Frodo makes his way onto the ship and turns back to smile at his friends, Sam is no longer wearing the yellow vest. The vest is still not there when the three Hobbits turn to leave the Grey Havens. When Sam is holding his daughter, he is once again wearing the yellow vest. On the Extended Edition DVD they explain this mistake.
In the Voice of Saruman, after Saruman has fallen onto the
spiked wheel it begins to turn, causing the Palantir to fall from his robe. When it is shown splashing into the water, the wheel is not turning, but continues to turn after the Palantir has landed on the ground.
In the "Voice of Saruman" scene, as the characters approach Saruman's tower, the waterwheel is to their left and parallel to their path. When Saruman falls on it, it has moved directly in front of the characters and perpendicular to their path.
When Frodo finishes writing the book, he reaches for the stab wound on his shoulder with the writing quill in hand. Then Sam walks in and in the next shot, Frodo's hand is still by his shoulder, but the quill is gone.
After defeating Shelob, Sam runs to Frodo. He lays Sting down next to him, on an area of dirt with a couple rocks sticking up. But later, when we see Sting glow blue, it's on perfectly level dirt ground.
When Saruman falls from the roof, he turns backward and falls top-of-body first, meaning that he is toppling counter-clockwise when viewed from stage left (the camera's view, in this sequence): In the brief moment showing him reaching the bottom of the tower (just before smashing on the water wheel), his body is toppling clockwise, still viewed from the left.
Nearing the end of the film where we see Frodo, Sam, Pippin and Merry having a drink at the Green Dragon, Frodo places four mugs on the table. The first sequence has two green mugs on the right and two brown mugs on the left. The second shot shows the mugs with a brown and green mug on each side of the table. Frodo puts the other brown mug in front of Merry, but in the next shot the other brown mug is in front of Pippin.
Toward the very end of the film, as Frodo finishes writing, he presses his hand to his chest. His quill is clearly visible between his fingers, and yet when the scene is cut to a slightly different angle, the quill disappears.
When Sméagol/Gollum falls into the lava, he sinks while the ring floats. In fact, lava, albeit a fluid, is sufficiently dense that a body would not sink into it, and rather sufficiently hot that the body would burst into flames. Metal, in the form of, say, a ring, is denser than rock and would sink, although it might melt before it sank very far.
Frodo is covered completely in a web cocoon when Sam grabs him and frees his face. Frodo's neck is still wrapped when the orcs take him. Sam somehow took the ring and chain from around Frodo's neck without disturbing the cocoon as he has it when he rescues Frodo later.
At the end of the movie when the four hobbits are at the Green Dragon and Sam works up the nerve to approach Rosie, Frodo has all 10 of his fingers. Gollum had bitten off the finger Frodo placed the One Ring on at Mount Doom.
In Mount Doom, after Frodo puts The One Ring on and Gollum jumps on his back, as they struggle, Frodo starts moving around. At some points in this scene, judging after Gollum's position on invisible Frodo's back, Frodo appears to be in mid-air.