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)
Continuity mistake: When Zorg is showing the the guns to the Mangalores, he is seen shooting the Police dummy, and when he turns to show them that every shot fired afterwards goes to the same place, he is seen starting to fire from his right to the left, but when the camera angle changes he is seen starting from the right again. (00:49:35)
Continuity mistake: When Corben bails on the 5-0 (in his taxi with Leeloo), he yanks the police car's winch right out of the car (which resulted in dragging the winch, as well as the entire length of the cable behind his taxi). In the next shot showing his car (4 police cars chasing him down the "street"), the cable and winch have disappeared. (00:36:00)