Mathilda never replaces the floorboard in her old apartment. When she is surprised there, she picks up the money and goes around the corner. The board would have been in the way and the hiding place obvious to the three men.
Leon erroneously uses the word "client" to refer to the person being targeted. A "client" is a person who hires Leon, via a "contract", to do a "cleaning" (killing) job, whereas a "target" or a "mark" refers to the one to whom a contract has been issued.
A bit more than half way through the film, Mathilda enters a Men's room with a bag of food sitting on top of a pizza. She stops, removes her sunglasses, the camera cuts to a wide-out of the bathroom, and almost immediately cuts back to Mathilda. When this happens, the sunglasses have completely disappeared, never to be seen again in the film.
The amount of milk seen in the reflection of Leon's sunglasses at his meeting does not reflect the amount of milk in the next shot. The reflection in Leon's sunglasses after setting the milk glass down on the table, when asked if he is free on Tuesday the glass is gone in his sunglass reflection.
Léon's milk rises and falls in his glass, depending on the camera angle, immediately prior to the charades game. He pours a less than full glass for himself when his back is to the camera, but it is at the top line when the camera faces him. As he talks with Mathilda, there are several shots back and forth with the level changing back and forth each time.
During Malthilda's first "hit" with Leon, she placed her handbag on the drug-mill table. Later the handbag was still on the table when she poured some fuel on the drug. But after she lit it up, the handbag was missing.
During Matilda's first "hit" with Leon, as Leon is instructing Matilda how to properly shoot the client, the client's position and body language against the wall, as well as his dialogue, are not consistent.
When Leon comes to the room he has blood on his right hand. When he gives Mathilda her present, there is no blood on his hand, nor when he answers the door for the hotel manager. He doesn't stain her dress either.
As Stansfield and his thugs search Mathilda's apartment, the dreadlocked thug played by Willi One Blood closes the turntable, lays his gun on it, and proceeds to rifle through the family's record collection. Although he is never seen to touch it, his gun points in a different direction each time the camera cuts back to him.
According to the headmistress's phone call, the Spenser School is supposed to be in Wildwood, New Jersey, but the end of the film shows that it overlooks Manhattan. Wildwood is a oceanfront community at almost the southernmost tip of New Jersey, over 150 miles from NYC.
Léon gives Mathilda a revolver, which she fires six times out the window. Later on (in the International version) she plays Russian Roulette with the same revolver, and we see her place three bullets into the cylinder, although the audio indicates she loads four. However when she spins the cylinder and before snapping it closed it can be seen that three out of five chambers are loaded. It would be impossible to fire the gun six times without reloading.
Many viewers believe that Stansfield never saw Leon, and therefore could not recognize him at the end, but they fail to remember that Stansfield visited Tony at the restaurant after Leon had killed part of Stansfield's crew. Thus, being intimidated and threatened by Stansfield, it must be presumed that Tony gave him a complete description of Leon, and very possibly a photograph.
When Matilda is watching The Transformers for the final time in the film, scenes from different episodes of the series are used straight after each other. This was a conscious decision by the filmmaker to use scenes to echo Mathida's state of mind.
When the fat man hangs up on his 911 call after Leon puts a knife to his throat, he pushes a button near the bottom of the handset to disconnect. The OFF button for that phone is at the top of the handset, not the bottom.
The goof items below may give away important plot points.
Immediately prior to Mathilda's capture by the SWAT team, she is holding the keys in her left hand. Even though she had no opportunity to change hands, they are in her right hand when she hands them to the SWAT team.
The "Rocket Grenade" that is fired through the door in the final chase sequence actually bears the NATO parachute markings of a paralume rocket, essentially a long burning flare attached to a parachute, not a high explosive projectile