Continuity: The match from the matchbook sounds like a wooden match when it falls after Dr. Walker checks his watch with it.
Continuity: When Walker climbs on the roof to Michelle's apartment, the suitcase comes open and her belongings pour out, sliding down the roof and to the ground many floors below. The Statue of Liberty model can be clearly seen flying over the edge, hitting the dormer of a window, and launching out into the courtyard. However, a few minutes later, once we have learned the statue's importance, it is still lying on that dormer, and Walker and Michelle must climb out to get it, risking their lives.
Continuity: The level of beer in Walkers bottle in the scene in the bar with the drug dealer changes from nearly full to half between shots.
Plot holes: In the airport scene with Michelle, Walker is terrified that the drug-sniffing dogs will find dope in their suitcase. Michelle assures Walker that there are no drugs, and the dogs walk by calmly. Walker seems to have forgotten that he's carrying at least a gram of cocaine in his pocket, which the police dogs don't notice either.