When Leon does an impression of John Wayne, he uses a hip holster for tin snips rather than a real gun holster. For all of his firearms, Leon would have no use for a pistol hip holster, since he needs to conceal his weapons beneath his duster, and his shoulder holsters aren't useful in a John Wayne impression.
Tony offhandedly points out that his "bank" doesn't have any forms to fill in. We find out when Leon is trying to check into a hotel that he's illiterate, so this would be helpful for Leon.
Léon is watching the hallway when Malky and Stansfield tell the old lady that they are from the police/DEA. Given the moment that follows where Stansfield shoots at the old lady, Léon knows that they might be Dirty Cops, and probably convinces Mathilda off-screen to distrust the police and to not answer the door when the NYPD does the usual interrogation of neighbors/witnesses.
Living next door to a police-guarded crime scene might endanger Léon's cover. Conveniently, Mathilda's shooting out of the window prompts Léon to leave.
Many people may find it odd that the grenade that sets off the bundle on Leon to kill Stansfield waited until after Leon finished his last words after handing Stansfield the safety pin. What people forget is that as long as the safety lever remained pressed down, you can pull the safety pin out and not have to worry right away about it detonating. The grenades were under Leon's vest, which may have been a tight fit, meaning that Stansfield opened the vest, it disengaged the safety lever on the grenade that Leon pulled the pin out of. Essentially, the vest Leon was wearing was keeping Stansfield alive and when he stupidly opened it to see where the pin came from, he sealed his own doom.
When Stansfield visits Tony and interrogates him for information on Leon, it's established that he used Tony in the past to hire contract killers. Léon was Tony's top hitman, and his "clients" were primarily drug dealers. Given all this, one suspects that, through Tony, a lot of Léon's jobs were, unbeknownst to him, actually jobs being carried out for Stansfield.
Malky says Willi Blood's name when Mathilda hears him mention her brother's killing. She later sees in the DEA building whom the other cops call Blood, and that Léon shoots him. Either she connects all the dots (which is rather Fridge Brilliance) or she fails to do so and spends her life with angry thoughts that their wrongdoer remained unpunished (Fridge Horror).
Léon tries to adapt Mathilda's teachings about acting out "no women, no kids" more consistently, but sadly his MO (and Mathilda's idea) is to kill. So during his "no women, no kids" initiative, Léon kills Malky, who was mostly trying to hold back the other thugs.
At least Malky's death is perfectly timed to stop Stansfield from killing Mathilda.
