Continuity mistake: When Lindsey is telling Slevin about taking the elevator with "Smith", we see her taking a picture of Smith, while pretending to have a phonecall. She makes a picture of Smith full in his face. When she's showing Slevin the picture she made, it's of the side of Smith's face.
Continuity mistake: When Slevin finishes shaving he wipes most of the shaving cream off his face and stares at himself in the mirror. There is still some shaving cream left on the underside of his chin and neck though. When there is a knock at the door the shot changes and the shaving cream has vanished.