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.
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).