In the penultimate scene in the temple, Ruby, unable to light the fire stone because he has no matches, claims that he would have some if he had not quit smoking. However, he is seen smoking earlier in the film, the cigarette being lit by one of his toadies: Ruby has not so much quit smoking as he has, being a galaxy-class VIP, quit lighting his own cigarettes.
After Rhuby Rhod's first broadcast in the airport interior, the commercial audio for the Gemini Crocket Contest runs in the background. Since Korben has already won, there is no need to keep running this commercial.
In the scene, where Corban Dallas is taking out the stones from the Diva's body and placing them into his jacket, sleeves on his shirt are alright, but right in the next scene, with this character, sleeves on his shirt are ripped and ragged, completely messed up. Scene, that is explaining, what happened with his sleeves is missing.
We see three Mangalores advance on Korben and Ruby in the first row right after Korben tells Ruby to guard the stones, then we cut to the President's office. When we cut back to Korben he has now shot three Mangalores at the front entrance to the Opera house and the arms of his shirt are now torn. There is no scene detailing what happened to his shirt or the Mangalores.
Zorg negotiates a deal with the Mangalores for some ZF-1 weapons in exchange for the Stones. One of them presses the red button causing a major explosion that would likely kill many of them. However later in the movie at the Phloston Paradise Cruising ship, the same Mangalores appear unhurt except for perhaps the right ear of the leader.
General Munro and associates are pushed into a freezer at Korben's apartment and are clearly frozen however later in the film General Munro is seen again. At no point is his unfreezing mentioned in the movie.
When Leeloo falls through the cab roof and Korben has to pull over and puts the cab on "automatic", the word "automatic" on the button is the wrong way down, but later when he pushes the button again to start running from the cops, the writing on the button is almost perfect.
In the scene, when Vito Cornelius tries to convince the president, the actor playing him has a little blood-spot on the right eye (as seen from the camera - it's his left eye actually). Later on - it disappears.
In the first scene where Zorg is walking, the sound of metal clinking is heard when his right foot hits the ground. After his face is shown, the metal clinking is heard when his left foot hits the ground for the rest of the movie.
When the Mangalores first bring the box of stones (which turns out to be empty) to Zorg, it shows him lifting the lid. It's obvious there is a frame cut at this point because the scene 'jumps' a bit to the right before he closes the lid again.
When Leeloo is exiting the shuttle on the cruise ship, the camera dollies forward and there is a crew member on the left of the screen with a radio. The camera quickly adjusts to remove him from the shot.
At the spaceport on their way to Fhloston, Korben takes David's ID, looks at it and calls him David when David is impersonating Korben. However, when David shows the fake ID's to Vito, he checks it and says "Korben David Dallas". When Korben shows up to the spaceport he takes David's ID looks at and since he knows David is not his middle name he just assumes his name is David.
When Leeloo has crash landed in Korben's taxi cab, when she looks up through the glass cab panel she has a strand of red hair across her nose and cheek that could be taken for blood, explaining why it "disappears" later.
After Leeloo has fallen into the taxi and is pleading with Korben for help, she sees a sign that says "Please help" and instantly understands how those two words are pronounced. For her, the alphabet should appear as gibberish and, even if she were able to realize that she was looking at writing and surmise the meaning, she should have had no idea how to pronounce it.
How do the Mangalores find out the stones were on Fhloston? We know Zorg learned of their location by bugging the President's office, but there is no scene showing how the Mangalores came by the same information.
When Leeloo is standing on the ledge and is being blinded by the police lights she raises her hands right before she jumps. Her hands are very dirty, almost completely black. After that she jumps down, crashes into Korben's cab, and puts her hands against the glass, here you can see her hands are much cleaner. Also her face seems less dirty.
In the first scene, when the Mondoshawans arrive to take the "fifth element" statue in the hidden room, the camera pans up and over the statue to an overhead shot. This statue has apparently been untouched for several hundred years, and would naturally be uniformly dusty. Unfortunately there is an obvious clean human hand print on the top of the statue, presumably from whoever put the statue in place for the shot.
In all shots of Leeloo up to the scene with Cornelius and David where she points out the planet to Cornelius on the monitor, there is a visible mark on her forehead (just above her left eyebrow) - not a dirt mark but an actual physical blemish on Milla Jovovich's head. However, just before the scene changes, it magically vanishes, and never reappears in the remainder of the movie.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
In the beginning of the movie when they are at the temple, the Mondoshawan gets stuck in the door of the secret chamber, however at the end of the movie when they re-enter the temple supposedly 300 years later, the Mondoshawan is completely gone with no trace. But you don't see the entrance to the temple so it is possible it is still there or since it has been about 300 years since the beginning it is possible that the Mondoshawans went back and retrieved their lost friend. Or that David found a way to move the Mondoshawan body when preparing the temple; obviously, he opened the door that originally crushed the Mondoshawan.