Plot hole: We see flashbacks to the first game in the context of Sora's memories. However, we hear Jafar speaking about how Sora found one of the keyholes. This was said during a meeting with the Disney villains at Hollow Bastion, long before Sora arrived there, so this scene shouldn't be included at all.
Continuity mistake: When Kairi and Sora finally meet again, Kairi hugs Sora. In the first shot, Kairi's arms are over Sora's. However, in the next shot, her arms are under his.
Trivia: In 'The World That Never Was' you come across a type of graveyard with the headstones acting as gateways to each of Organization XIII's members' rooms. Each headstone describes their respective member with a depiction of their respective weapons.
Answer: Although it remained unclear where Kairi went during the events of Kingdom Hearts 2/Final Mix, it is safe to assume that she stayed on the island until Axel kidnapped her, only to be taken from Axel's hands by Saix. This event was mentioned during the Heartless massacre (inside the portal connecting the "fake" Twilight Town with The World That Never Was), where she ended up meeting Naminé before reuniting with Sora and Riku in that world.
YetiSsimo