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.
Revealing mistake: When Qui-Gon is attacked by Darth Maul for the first time, he escapes by leaping onto his ship which quickly takes off. As they zoom up into space, he discusses the mystery attacker with Obi-Wan. However, the lighting from outside the windows never changes giving the impression that they are static on a set rather than whizzing up into space.
Revealing mistake: When the Queen is escorted down the stairs in the Theed Royal Palace, right before Nute Gunray says, "Process them.", watch the space between Sabé (the Queen's decoy) and Captain Panaka, before a handmaiden and one of the Queen's guards block the view; the battle droid behind Sabé doesn't cast a shadow on the railing, as everyone else does in this shot.
Revealing mistake: When Qui-Gon and Obi-Wan are being gassed, Nute Gunray's hologram says, "Destroy what's left of them." After he says this, watch the battle droid on the left side of the screen closest to the hologram. One of its fingers goes through the barrel of the gun it's holding.
Revealing mistake: During the second lap of the Podrace, the announcer says, "Skywalker's spinning out of control" and there's a shot of the audience. After Anakin has won the race, the same shot is used again. This can be seen, for example, from that the people on the steps make the exact same movements in each shot.