Major Plot hole: Leeloo loses all hope in humanity when she finally learns the definition of War. She had to go through all the words from A to W before being outraged. Which is funny considering she read and learned words like: assassination, holocaust, murder, lie, nuke, terrorist, hostage, torture, rape, genocide, sin, execution, hatred, racism and laugh track. This short list also does not include the hundreds of words that are part of war itself, such as: gun, tank, battleship, soldier, missile, general, and so on.
SO, how is it even remotely possible for Leeloo to 1- not learn the word War even before reaching the letter W ?, and 2- not be disappointed by humans a few letters back ?
Plot contrivance: In the future, bomb detectors exist. However, if a bomb is planted and timed to blow up in 20 minutes, the alarm will start 5 minutes before it is meant to explode. Why ? Don't look at us, ask Luc Besson.
Unaddressed Issue: Halfway through the story, everyone is converging to a luxury cruise in order to obtain the 4 stones that are part of the weapon to stop the Great Evil. The term 'everyone' includes the Mangalores who were never shown to know where the 4 stones were supposed to be. Zorg knew because he had a man working to listen to the President's secret discussion with the military and Korben knew because Leeloo told him. But the Mangalores had no clue of this. Why were they present at the airport with one of them pretending to be Korben Dallas ? Don't look at us, ask Luc Besson.