As Darth Vader leads the 501st Legion up the steps of the Jedi Temple you can hear their steps, marching in perfect unison, yet you can see that their steps not only do not match the audio, but they are not in sync with each other either.
When Padme is trying to convince Anakin to turn from the dark side on Mustafar, when Anakin says "And I'm doing it for you, to protect you." his mouth says "And I'm doing it because I love you, to protect you."
After Anakin informs Mace Windu about Palpatine in the hangar, as he follows him to the ship nearby, Mace tells him not to come with him. When you hear Anakin respond "I must go, Master," his mouth is saying something different.
When Obi-Wan and Anakin are having their exchange of words following the landing at the Senate building, there is a strange echo when they speak to one another. Neither one is indoors, and there's nothing nearby to create an echo since they are using regular speaking voices.
Just before the fight scene between General Grievous and Obi-Wan, Obi-Wan uses the force to drop a large vent-like object on top of Grievous' guards. In the fight scene that follows however, the object has disappeared.
In the final battle between Obi-Wan and Anakin, the river of lava reverses direction of flow. When Obi-Wan jumps off the platform, the river flows towards his right, but in the next shot of Anakin, it is flowing towards Obi-Wan's left.
When the Emperor is pushed back by the force lighting collected by Yoda, he barely holds onto the smooth senate pod to keep from falling. In the next shot (after Yoda has fallen), he's holding onto a metal bar that wasn't there before.
When Anakin and Obi-Wan are struggling on the table on Mustafar during the final battle, Obi-Wan constantly switches from holding his to Anakin's lightsaber in his right hand.
During the Final Battle on Mustafar, while the massive Metal Platform is going over the lava fall, there are some shots where Anakin's glove switches hands, and both characters switch their light sabers from hand to hand between shots.
When Yoda uses the force to send Darth Sidious flying across the room, Sidious lands in his desk chair which knocks over backwards. In the next shot where the desk is visible, the chair is standing back up again.
When Anakin is on top of the elevator, getting ready to jump back inside of it, you can see for a moment that the glove is missing from his prosthetic hand, yet after he jumps and is back inside the elevator, the glove is back on.
When Obi-wan and Anakin enter the elevator on the Trade Federation flagship, they kill several battle droids. In every other take shot in the same elevator, there are no parts left on the floor. The part of the ceiling that Anakin cuts out also disappears. Also, when the elevators stops the first time, a Battle Droid's hand can be seen standing in the left corner, however, when the shot changes, it disappears and then re-appears again in a shot near the end of the sequence.
When Mace is approaching the prone Emperor along the broken window ledge, the Emperor scoots backward up to the window frame behind him and Mace stands over him. The camera angle changes to Anakin, and behind him the Emperor is still scooting and Mace is still advancing.
The Bridge crew of the Invisible Hand evacuate the area twice. They start to leave after the Guard Droids are defeated, as evidence by all the empty crew stations when Grievous is making his exit through the window. Then after the windows explode and Grievous is blown out into space and the shutters close, we see another interior shot with the crew again running out of the bridge after it decompressed.
When Palpatine takes out his lightsaber during the battle with Mace Windu, the unique design of the handle can clearly be seen. When he engages Mace and the Jedi, although the blade is still red, the handle of his lightsaber suddenly changes to Anakin's large clunky handle.
When Mace Windu gets on the air transport and tells Anakin to stay behind, the shadow of the vehicle disappears in the shot when Anakin is seen alone, but reappears in the next shot when we see the vehicle take off.
When Yoda enters a room to confront Darth Sidious and knocks the two guards unconscious using the force, the position of the guard's bodies shift during their fight scene and are positioned (conspicuously conveniently) out of the way.
Throughout the fight scene between Sidious and Yoda in the Grand Chamber, the pattern of the chairs change. In some shots, the chairs on the wall are in straight lines, but in other shots they are placed every-other.
when in the beginning of the film, Anakin, Obi-Wan and Chancellor Palpatine are falling down the elevator shaft, Chancellor Palpatine is holding Anakin by the leg at the beginning, then with the next cut he isn't, then when they swing into the corridor he is once again holding on.
Dooku tries to choke Obi-Wan and sends him flying across the room with his left hand while holding his lightsaber in his right hand. In the shot where Dooku uses the Force to crush Obi-Wan with the large metal platform, he uses his right hand, which should be holding the lightsaber. The lightsaber is then in his right hand again when Anakin kicks him off the balcony.
After Mace Windu disarms Palpatine, Mace advances on Palpatine
with his blade held out, while Palpatine backs into the corner of the window in his office. In the next shot, when Anakin enters the office, Mace is shown advancing on Palpatine again.
In the final battle between Vader and Kenobi they are fighting on the platform that has fallen into the lava river. Just before it goes over the edge, both Vader and Obi Wan swing from cables and slash at one another. Obi Wan jumps onto a small floating piece of debris, the next shot shows the platform about to fall over the edge clearly with the view of a light saber in the middle of the platform. The next shot shows Anakin just swinging back to the platform as its falling over.
During the first part of the escape from the Invisible Hand, when the decks tilt, objects (such as R2-D2, for instance) lose traction and slide "downslope". This would not happen on a ship in which an artificial gravity field was in use. "Down" would always be straight towards the deck, no matter how the ship was oriented with respect to its exterior surroundings. The sliding objects on the ship behave as if the source of gravity was outside and below it. Of course, without internal artificial gravity, everything on the orbiting ship would be in freefall.
When the buzz droids are destroyed on Obi-Wan's fighter, they are swept away as if by wind flowing over the wings. As there is no air in space, the wreckage of the droids should have remained on Obi-Wan's fighter.
Throughout the movie, Mustafar is described as a "volcanic planet", yet in all of the exterior space shots of the planet, we see it orbiting extremely close to a very large gas giant. There is no way a small planet like Mustafar could maintain its own orbit around its sun so close to a gas giant as depicted in the film without the gas giant having a major gravitational effect on its orbit. It would have been much more realistic (from a physics point of view) to describe Mustafar as a large moon orbiting the gas giant planet, much like the moon of Io orbiting the planet Jupiter in real life.
During the opening sequence, the destroyed buzz droids drift off of Kenobi's starfighter as if blown off by wind. However, since this is in space, a vacuum, they would have sat on his wing until movement by the ship, such as a bank, would have tossed them from their place. Wind would not have done it though.
Just after Order 66 is given, the zipper in one of the Wookie costumes (the one on the right hand side of the screen standing behind Yoda) has been said to be visible. In fact, it is merely part of the background peeking through the Wookie's legs.
Much of the computer-generated light sources do not cast light on the very real actors. For example, when General Grevious has a light saber in Obi-wan Kenobi's face, and then Chewbacca (near the end) is very close to Yoda's single-person spacecraft taking off with jets firing.
General Grievous, whose two arms can split into four, has a total of twelve fingers (six on each hand when his arms aren't split). However in some shots (such as when he orders his ship's bridge crew to fire the emergency booster engines in an early scene) we can clearly see he has five on each hand when his arms aren't split. In other shots, he has the correct number of fingers.
In the duel between Mace Windu and Palpatine the camera shots are obviously alternating between those of Ian McDiarmid, playing Palpatine and those of the stuntman, who does not look much like the actor he is standing in for.
When Palpatine battles Mace Windu and his fellow Jedi Council members, Palpatine's lightsaber handle changes to Anakin's handle. This is because the scene was originally shot with Palpatine using Anakin's blade.
At the beginning of the movie when the two super battle droids are searching Anakin's fighter, the quick shot of them looking to R2-D2 is reversed as their red sensor is located on the opposite shoulder.
The goof items below may give away important plot points.
When Obi-Wan jumps onto the small, metal platform in the Mustafar river, you hear the hum of a lightsaber, even though it is not ignited. When he regains balance, he turns it on, and it sounds as if it was on the whole time.
Padme dies in childbirth. However, in Star Wars: Episode VI - The Return of the Jedi, after Luke and Leia realize they are siblings, Leia claims to remember her mother - in Return of the Jedi, Luke clearly asks Leia about her "mother, your real mother" - indicating she was not in fact talking about her adoptive mother. It is possible, however, that Leia did not know she had been adopted.
In the final sequence on Tatooine, when Obi Wan is handing the infant Luke to Beru, he opens his cloak to bring the baby out as he approaches her. This is first seen in a long shot from above. There is a cut to a two-shot, and he opens his cloak and extracts the baby again.
During the Jedi purge sequence, the cockpit of Plo Koon's Jedi Fighter does not match the exterior shot. (The cockpit is the Revenge of the Sith 'Eta-2' model, the exterior is a 'Delta-7' from Star Wars: Episode II - The Attack of the Clones.)
After the fight between Obi-Wan and Anakin, when Obi-Wan gets back into the spaceship, his clothes are completely clean, without any soot or ash or dirt on them. Later on, when he is talking with Yoda about the babies and going into exile, there are obvious dirt and burn marks on his clothing.
Later in Star Wars: Episode V - The Empire Strikes Back Obi Wan disbelieves that "there is another", with the implication is that Yoda was speaking about Leia, about whom Obi-Wan should have known. In the context of "Empire", Obi-Wan had written off Leia as a prisoner of Darth Vader, whereas Yoda believed she would escape and continue the fight.
On the landing platform at the Jedi Temple, during the eradication of the Jedi, Bail Organa observes a young Jedi Padawan get shot by Clone Troopers. In Organa's escape, he jumps into his speeder with his left hand gripping the steering control. In doing this, he turns the control all the way to the left. Yet, his speeder moves forward in a straight line, ignoring the input.