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When Anakin first uses the laser cannons on the Naboo Starfighter to destroy the Droidekas in the Theed Hangar, the lasers make the sound effect of Proton Torpedoes (as seen and heard later, when Anakin is firing inside the hangar of the Droid Control Ship), not laser cannons (which, again, sound different in later scenes with Naboo Starfighters).
In the Nubian parade scene at the end of the movie, Anakin Skywalker is seen as a Jedi Padawan and sports a new haircut and a Padawan braid. The braid is considerably longer than his hair had been at any other point in the film.
When Jar Jar activates the Pit Droid in Watto's shop, he knocks over a protocol droid and some other junk. A moment later the droid is upright again.
During the fight over and around the droid control ship, Anakin says to R2-D2, "I'll try spinning, that's a good trick." Anakin is seen to turn the flight controls to the left, but his craft spins to his right. In an earlier scene (right after the auto pilot is disconnected) Anakin says, "Let's go left", turns the controls to the left, and the scene tilts to Anakin's left.
When Anakin and Padmé arrive at the pod racer hangar, Anakin is taller in the close-up shots, and Padmé's hair is noticeably a little different. The close-up shots were done almost a year after principal photography.
Upon the Queen's landing to meet the Senate there's loads of air traffic, yet when they land, there's no reflection of any of the ships flying overhead on the shiny ship itself.
When the engines start turning on Anakin's pod racer, they are turning the wrong direction. They should be turning so that the fan blades will force air into the engine, but the direction they are turning, air will blow out the front of the engine.
The opening crawl states that two Jedi knights have been sent. But only Qui-Gon Jinn is a Jedi knight. Obi-wan Kenobi is a Jedi padawan, training to become a knight.
R2-D2 is lifted into a Naboo N-1 Starfighter from below. His entire head appears out the top, sticking out of a short cylindrical part of the ship. This would be impossible, as there is no room within the cylinder for his legs to fit.
Some naturalists have stated that Watto's wings weren't big enough to lift his body in flight. George Lucas explains that Watto's digestive system filled his rotund belly with helium, making Watto a blimp, not a bird.
It is established early in the film that Qui-Gon Jinn and Obi-Wan Kenobi have the ability to dash several feet across in a few seconds, yet it never occurs to Obi-Wan to use that power in the hallway with the revolving force fields to reach Qui-Gon and Darth Maul in time. Of course, if he did, he could have crashed right into a force field, as they turn on and off so quickly.
When listing candidates for Chancellor, Captain Panaka includes "Bail Antilles of Alderaan." In other movies, there is "Bail Organa of Alderaan". However, there is nothing unusual about two men from the same planet having the same first name. Printed materials explain that these are indeed two different characters.
During the final lightsaber battle, the red force fields can be regularly seen opening and closing before Obi-Wan emerges from them. After he does, they cannot be seen or heard opening or closing again. However, the force fields are not necessarily on permanently and may have simply finished a regular or semi-regular cycle when Obi-Wan emerges from them.
As the Jedi run from the droidekas, they disappear (or at least become very faint) briefly. This is a deliberate effect to indicate the speed of their departure.
As Qui-Gon, Padme, and R2 enter Anakin Skywalker's home, Qui-gon introduces himself to Anakin's mother and as he says, "I'm Qui-Gon Jinn", Padme mouths these same words. This might not be visible in the pan and scan version of the film.
When Sebulba is on the verge of running down Anakin during the pod race, there is an over the shoulder shot clearly showing that Sebulba's pod is unmanned. An acknowledged animation error.
When Qui-Gon and Jar Jar are eating the meal at Anakin's house, his mother goes around the table pouring water into everyone's cups. She pretends to pour it into Jar Jar's computer-generated cup, and it sounds as if she does, but no computer-generated water has been added into the scene.
There is a support bar visible between R2-D2's legs before the gang enters Watto's junk shop.
When Darths Maul and Sidious are conversing on Coruscant ("At last we will have revenge!"), Maul's neck is visible beneath his cloak, and is flesh-toned. Everywhere else in the film, his neck is black.
When Qui-gon and Darth Maul was fighting on Tatoonie, when Obi-wan was looking out the window of the star ship, Darth Maul and Qui-gon had the same light saber color.
In some shots of Natalie Portman when she's with Liam Neesom she is mouthing Liam's lines.
After Daultay Dofine's first line of dialogue ("I knew it! They're here to force a settlement!"), he and Rune Haako switch voices. For the rest of the film, Haako speaks with Dofine's voice, and vice versa.
When Darth Maul and Obi-Wan are fighting at the end of the film, Darth Maul hits Obi-Wan's light saber three times but there are four clashing sounds.
After Anakin has won the podrace, he yells, "Mum, I did it! Yeah!", but the words don't match his actual lip movement.
After the transport is destroyed in the hangar, near the beginning of the film, the scene cuts to Obi-Wan and Qui-Gon. The sound of their lightsabers being activated occurs before they even draw them from their belts.
Before the Trade Federation Droid Control Ship starts exploding from the inside, a Neimoidian says, "Nothing can get through our shield". But his mouth doesn't move until after he's said it.
When Darth Maul takes his speeder bike after finding the missing Jedi, you can see a pair of tire tracks from a car or truck.
When the droid army is entering the city, it cuts to the scene where the Queen is looking out of the window in her palace. As she approaches the window, there's a large ILM (Industrial Light & Magic) sign written in what looks like red spray paint at the bottom right hand corner of the screen.
In the Boardroom in Otoh Gunga, as Obi-Wan and Qui-Gon turn to leave, you can see Obi-Wan's lapel mic just inside his tunic.
When Anakin is in the hangar begging Qui-Gon to let him come with them, a yellow stick with a ball on top disappears from the background.
When Queen Amidala is standing before a big window, watching the Trade Federation enter the city, she is wearing a dress with lights at the bottom. Behind her the power cable of those bulbs is visible.
How do they get from Naboo to Tatooine in such a short period of time without a functioning hyperdrive? In maps of The Galaxy, and using material from the games and comics, Naboo and Tatooine are roughly 4,500 parsecs (14,677 light-years) apart. At sub-light velocities (maximum sub-light speed is 0.25c or 1/4 the speed of light) it would take roughly 58,700 years to travel from Naboo to Tatooine.
As Darth Maul lands on Tatooine, in the night sky is the Earth's view of constellation Orion.
As Qui-Gon is weighing his options for payment, Anakin states, "there's a big race tomorrow..." However, the race is the day after tomorrow, as Anakin spends the next day getting his pod ready for the race and another evening follows.
Queen Amidala slips just after they have captured Nute Gunray in the throne room.
When Anakin's fighter travels into orbit, R2-D2 puts a message on the screen telling him to turn the fighter back 'homie', instead of 'home'.
After Darth Maul is chased into the large room with the chasm by Obi-Wan and Qui-Gon, he backs off to the edge and the camera goes back to a more distant angle. At that moment, Darth Maul seems to almost stumble into the chasm and quickly catch himself again.
When a racing pod crashes, Beed Annodue states "I don't care what universe you're from, that's got to hurt!" The word "universe" makes little sense in this context. Perhaps he meant planet, system, or galaxy.