Leon: The Professional, the title is pretty clear. It's about a professional hitman, Leon, whom Jean Reno portrays in the film. His skills are impeccable, no matter the approach, stealth or simply chaos. When active, he can appear from the dark corners or stick near the ceiling like Stellan Skarsgard's Baron Vladimir Harkonnen does in Dune: Part One.
He has all the skills an assassin needs, but his quality of sticking to the rules is what makes him a 'professional.' That said, professionals have rules, and they don't simply act on their emotions to enter a premises, kill a few men, and bring back the supporting character of the film within minutes.
At least that's not what hitmen do in broad daylight, especially in the Drug Enforcement Administration (DEA) building. But Jean Reno's Leon does exactly that, which is one plot hole of the Luc Besson film. Though not really big, it is a well-connected element in the chain of events of the story.
Why does Leon break into the DEA building?

The film has given the fans one of the best antagonists of all time, the maniacal DEA agent Norman Stansfield, whom the brilliant Gary Oldman plays. This guy has killed the family of a girl, Mathilda (Natalie Portman), including her four-year-old brother. Leon saves her from being killed.
Now she is seeking revenge for this and asks Jean Reno's Leon to teach her the tricks of his trade. He does that, though it takes Mathilda some convincing, and during the process, they develop an unlikely bond.
Although she isn't exactly prepared, she fills a grocery bag with guns and enters the DEA building to find Stansfield. However, she fails to do that, as Stansfield catches her off guard when she is looking for him. She is almost killed but thanks to a phone call, after which Stansfield takes off, she is held captive in the building.
Before leaving from the apartment, Leon and Mathilda are staying at, she has left a note explaining everything. Leon acts impulsively to save her and breaks into the DEA building and brings her back. It seems like he simply walked like it's no big deal, killed a few cops and brought Mathilda back, just like that. There at least needed some tensions to accommodate a scene like that.
And Jean Reno's character didn't really make his cab driver wait outside the DEA building, who was reacting rudely after waiting for "ten minutes."
Another scene where Jean Reno's character is trying to escape somewhat accommodates this plot hole

After all this happens, Stansfield gathers "everyone" (hear that scream?) to kill this pro and they manage to infiltrate Leon's apartment. However, Leon is smart, and he swaps his clothes with the uniform of a dead DEA agent and escapes using an excuse for being in need of a medic.
It is one intelligent move, given the fact that the staircase is filled with the law enforcement squads and Jean Reno's character is no Daredevil, who specializes in clearing such a blockade.
This scene accommodates Leon's DEA break-in scene to some extent. Even if he is not in shape after the final fight, he knows what to do when law enforcement is around. But this time, Mathilda is safe, so we can say there are no impulses involved here.
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