Audio problem: When the stewardess is telling the people that she's putting on the sleep regulator, they show a different shot, and you see in the background she's mouthing words that don't match up. (01:15:25)
Continuity mistake: When they are trying to place the stones in the temple, Korben picks up either the water or air stone - by the time they get to the plinth he's holding the fire stone. (01:53:15)
Continuity mistake: When LeeLoo is on the ledge outside of the building, the police corner her & take her picture. Her face is pretty calm, but when the picture is developed on the police screen, she looks shocked. (00:32:20)
Continuity mistake: During the missile barrage on the dark planet, one of the soldiers says, "The planet has increased in diameter by 200%." That means that the diameter would be triple the original size, but it's obvious from the missile impact animations that it hasn't grown anywhere near that much. (00:16:30)
Continuity mistake: When David is waiting for the priest and Leeloo before attempting to board the shuttle to Phloston Paradise, he is chewing on the nail of his index finger. The shot changes to show a different angle of him and he is now chewing on his thumbnail with no time for him to have changed position.
Continuity mistake: The shadow of the dark planet is heading in the direction of the sun, instead of away from it, in the scene where the dark planet is approaching the temple. (01:54:55)