Continuity mistake: When the police confront Leeloo on the side of the building, she raises her hands and we can see that they're covered in soot. She jumps off and lands in Korben's cab. When she comes to, she presses her hand against the glass, and her hand is magically clean.
Revealing mistake: Right after they "create" Leeloo and she is lying in the plastic cage with the little straps on her, the guy approaches her and says, "if you want out, you are going to have to work on your communication skills." She gives him a dirty look, and then you can see a huge hole, pre-cut in the glass, that she busts her hand through.
Continuity mistake: When Zorg is first seen walking, and the screen only shows his legs, there is an audible clank as he steps with his RIGHT leg. After that, the clank is heard from his left foot.
Continuity mistake: When the cops go looking for Korben and Leeloo in the fog, there are two orange light sticks hanging from the ceiling inside their car. From the outside looking in they are swinging from side to side very quickly. But from the inside looking out they are swinging from side to side very slowly.
Continuity mistake: When the police are chasing Korben and Leeloo in the taxi, Korben uses a video display map of "Manhattan 2nd District". When he switches it on, it looks normal, but when the camera cuts away then back again, the display is reversed as though it were in a mirror.
Continuity mistake: After Leeloo fights the Mangalores in the Diva's room but then has to give the stones box to Zorg, she throws it to him with forward rotation but when the box is shown flying through the air in slow motion, it's rotating backwards.
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.
Continuity mistake: In the scene in the beginning when you first see the fifth element, and the camera moves up so you see the wide open mouth, look to the shoulder on the left. In the years of undisturbed dust, there are a few finger prints.
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.