Continuity mistake: During the podrace, Anakin is in front of Sebulba and has him on his tail. One view looking towards Anakin you can see Sebulba's pod in the background, but the driver's seat is empty.
Revealing mistake: When Qui-Gon, Jar-Jar, and Padme are eating at Anakin's house, Anakin's mum pours water for Qui-Gon. But when she gets to Jar-Jar, she tips the pitcher but no water comes out.
Continuity mistake: Obi-Wan's braided hair keeps changing sides, and getting longer and shorter, most noticeably in the scenes around the underwater city.
Continuity mistake: When the flags are first brought out onto the course, we see C3P0 carrying Anakin's flag (a blue cross) three back from the front. Then in a closeup of him, he's suddenly between two different flag carriers. Worse still, in a wide shot of the flag carriers leaving the course before the race, he and the flag have disappeared completely.
Continuity mistake: When Anakin attaches 3PO's right eye, one shot has the eye in his left hand, then the angle changes and the eye is being applied with the right hand.
Continuity mistake: When Palpatine and Queen Amidala are conversing in his office (when Palpatine refers to Valorum having 'very little real power') his outfit switches from a green breasted cloak with a blue collar area to a green breasted cloak and dark green collar. It switches back after one shot.
Continuity mistake: When Amidala and some other guards use the ascension guns from the palace windows seven of them go up, when they are running along the corridor after coming off the window-ledge, there are about 13 or 14 of them. Then finally when they are surrounded by the droids, there are about 10 or 11 of them and Captain Panaka is not there.
Visible crew/equipment: In the initial scene, when the Federation invade Naboo, you can see two takes of Queen Amidala watching the window on her palace. At the left of the screen you can see a black wire - maybe a light connection?
Audio problem: 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.
Continuity mistake: Darth Maul's neck is black, but when he is talking to Darth Sidious on Coruscant, his neck is flesh-toned.
Continuity mistake: In the chamber room near the end of the movie, after the Queen throws the guns to everyone and goes to address the Viceroy, she starts to walk away from her chair. While she is doing that, you can distinctly see her lose her footing and slip on the floor. In the next edit she repeats this movement without slipping.
Revealing mistake: After everyone leaves Tatooine after the short stay they land on Coruscant in the middle of busy air traffic. Unfortunately, the ship that they fly in (the Nubian), with its incredibly shiny and mirror-like appearance does not reflect the bustling traffic above, nor the people walking out of it. It only seems to reflect the basic landscape.
Continuity mistake: When Qui-Gon and Obi-Wan are landing the Naboo ship on Tatooine to repair it, watch the landing closely. The shadow of the ship is already on the ground before the ship lands on it. Also the ship tilts back and forth during the landing but the shadow never changes or moves. Also, if you look carefully at the dust (which was shot using a helicopter landing) some of the dust being flicked up actually passes through the ship.
Revealing mistake: When Qui-Gon is talking to Jar Jar for the first time, they are walking through the forest. A branch with leaves comes up and Jar Jar dips his head to avoid it, but his eye and part of his head go through the leaves.
Audio problem: After Anakin has won the Podrace, he yells, "Mum, I did it! Yeah!", but the words don't match his actual lip movement.
Revealing mistake: When the Queen blasts the window to gain entrance into the upper floor of the palace, a shot from down the corridor reveals that the window was already open before the sparks and smoke appeared on screen.
Deliberate mistake: When Jar Jar gets arrested in the Gungan city, in the second shot of Jar Jar and Obi-Wan, Obi-Wan and a part of the floor behind him are reversed. This can be seen, for example, because two of the red areas on the floor have switched positions, and Obi-Wan's braid and lightsabre are on the wrong side.