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)
Revealing mistake: Whilst Diva Plavalaguna is singing, you can see the back of her head creasing and bending. This is because the suit that the actress is wearing is made out of foam latex; confirmed by Nick Dudman, Creature Design Supervisor on the DVD featurette "An Audience With Diva Plavalaguna".
Revealing mistake: After Korban meets Ruby and everyone leaves them alone, Korban grabs Ruby by the neck and holds him to where his feet can't even reach the ground. In the first shot, you can tell that Korban's hand isn't even applying pressure. In the next few shots of Ruby, still being held off the ground, you can now see that Korban's applying a little pressure now, but probably not as much as there should be while holding a full grown man a foot off the ground.
Audio problem: During any scene where weapons are being fired, the audio has the sound of cartridge casings falling onto a hard surface, but none of the weapons are ejecting cartridge casings to fall.
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)