Continuity mistake: After Leon rescues Mathilda from the SWAT team and dodges the snipers, he shoots out a ventilation fan to make an escape route. He gets off two shots before we see the vent, but when it does we see about 7 bullet holes around the vent. Then the camera goes back to Leon as he continues firing. When the camera switches back, the holes around the vent are different. (01:27:05)
Continuity mistake: In the very first scene where Old Tony is debriefing Leon, we see Leon pick up his glass of milk and drink the entire glass. However, if you look at the reflection of Leon's glasses as he takes the glass away from his mouth, you can see that the milk is not finished. (00:02:30)
Continuity mistake: Before the dreadlocked man starts looking at the vinyl records in the apartment, he places his uzi down with the butt facing the camera. In the next shot the barrel is facing the camera, and switches back again in the next shot.
Continuity mistake: In the scene where Mathilda returns to her apartment and takes the hidden stash of money out from the loose floor board, she leaves the board open and also takes the money out of the plastic bag and leaves the bag on the floor too. In the next shot, the camera angle switches to her looking down the hall because she hears people coming. When the camera switches back to the original angle of her scurrying away, the floor board is back in place and she's wrapped the money back up in the plastic - nowhere near enough time to do that. (01:02:25)
Factual error: The grenade that the SWAT team fires in the hotel is supposedly a smoke bomb, but it is both marked ILUM and has a white body, meaning that it is an illumination grenade.
Continuity mistake: When Mathilda hides the cigarette from Leon it's practically new, but in the next shot (when Leon asks her why she hid the cigarette) it's almost finished. However, in the next shot it's practically new again.
Continuity mistake: When Mathilda spends her first night at Leon's apartment, Leon places a messily folded blanket on her in one shot. The camera then goes to a different shot of Leon, and then back to the original. However, we can now see that the blanket is mostly unfolded and placed neatly on Mathilda. ..... (and little pink doll she is holding changes position). (00:37:15)
Visible crew/equipment: When the SWAT team fires the grenade into the apartment at the end, the guide wire along which it is traveling is very obvious. It's actually easier to see in normal speed. (01:29:25)
Continuity mistake: At the beginning of the film, the intended target calls 911, with the phone's aerial fully extended. The shot later it's half the length. (00:07:00)
Continuity mistake: Leon is playing with Mathilda and she can't guess the actor. she tilts her head and then angle changes to the back of her head. But now not only her head is not tilted but when she says "I swear, I was going to say that actor" she is not mouthing the words.
Continuity mistake: When Leon shoots out a ventilation fan to make an escape route he stands right in front of a window. In the previous scene snipers were shooting at him, why are there no snipers shooting now? (01:26:20 - 01:27:10)
Continuity mistake: In the scene where Matilda is expressing her feelings to Leon, she lies on the bed and her hair falls in two separate strands, by the next shot (although she has been motionless on the bed talking), her hair is neatly spread.
Plot hole: Towards the end of the movie, Leon dies and Mathilda heads to see Tony. Tony gives her some spending money and tells her to get back in school. The nighttime scene suggests that she spends at least part of the night wandering the streets. Presumably at daybreak, she takes the tram car and returns to The Spencer School, where she talks to the school administrator. When the administrator asks Mathilda to tell the truth about what happened to her, Mathilda says in essence, "... I lived with the greatest guy. He was a hitman, the best in town. He died this morning..." This morning? Seems more like roughly 24 hours have passed since Leon died, so what Mathilda says is inconsistent with the scene sequence. (Special note - this is from the International/extended DVD edition. I can't say whether this exact sequence is in the shorter domestic DVD version.) (02:06:03)
Continuity mistake: Mathilda's school switches from being in Wildwood, NJ (at the start) to being on Roosevelt Island, NY. (00:18:15 - 01:38:15)
Continuity mistake: In the scene where Leon shoots out the ventilation shaft, you can see bullet holes through the wall, but when he starts to use the axe on the wall, in the next shot from inside the ventilation shaft the bullet holes have disappeared.
Other mistake: When Leon enters the apartment building in the first shots he, needs to go up the stairwell in order to get to his apartment. But in the scene when Mathilda enters the building (after getting groceries while her parents got shot), she's right on the apartment floor without having to use the stairwell in the first place. (00:20:00 - 00:30:00)
Revealing mistake: After the SWAT team grab Mathilda, the guy who grabbed her backs up against the wall and it bends inward, revealing it to be a set.
Visible crew/equipment: Near the end of the film Leon tells Mathilda to grab the axe. As she opens the glass door to get it you can see the camera and its operator filming reflected in it.
Answer: According to IMDb.com the title was only changed in the United States and the reason why was maybe audiences would find the title, "The Professional" more appealing than "Leon."