Plot hole: At the end of the film Mardukas reveals that he has been wearing a body belt packed with cash - "in the neighbourhood of three hundred thousand dollars" - ever since Jack detained him in New York. Are we to assume that Jack Walsh, an experienced, hard-bitten ex-police officer, now a bounty hunter who routinely chases down violent and armed bail absconders who would kill him without a second thought, didn't even perform a perfunctory search of Mardukas when he detained him? This man used to work for the Mafia! What if he was carrying a weapon? A body belt with three hundred one thousand dollar bills in it would be uncovered by even the most casual pat down.
Continuity mistake: At the beginning of the movie when Tony and Joey (Morons #1 and 2) meet Jack Walsh at the car rental desk, Tony writes a phone number on a packet of matches in pencil. Near the end of the movie when Jack Walsh fishes this pack of matches from his pocket, the phone number is written in pen.
Continuity mistake: When Jack and Jonathan are sitting in the carriage on the first train, Jack holds a pad in his left hand and a pen in his right. He then lights a cigarette. In a sequence of shots, his right hand is holding the pen, the cigarette or both together. At no time does he change either item to his left hand.
Continuity mistake: When Jack and Jonathan got off the bus, Jack holds in his hands a brown folder or dossier (I guess the script) when they were about to be arrested against the bus. The second after there is no such folder.
Continuity mistake: When the Duke falls into the water he has a pair of handcuffs only on his right wrist. When he is shown flowing downstream he has the cuffs only on his left wrist. The next shot where his hands can be seen the cuffs are on the right wrist again.
Continuity mistake: When Jack Walsh is in the diner after losing the Duke to Marvyn he can't light his cigarette with his lighter the man behind the counter gives him a pack of matches and say "keep them", but when Jack brings the Duke to LA airport he comes down the escalator and lights up a cigarette with his own lighter.
Continuity mistake: Jerry Geisler is at his desk just about to light a cigarette when Jack Walsh calls on the phone. Geisler angrily slams down his cigarette and lighter to answer the phone. In the time it takes him to say "Eddie, it's Jack" he has picked up both the lighter and cigarette and lit the cigarette.
Plot hole: There is no way Agent Mosely could not know that he didn't have his identification, he would need it to get in and out of FBI headquarters as well as it being standard procedure to show his identification when announcing that he is an agent.
Plot hole: When Jack and The Duke are told to leave the plane they are still in New York, they then get train tickets from Grand Central Station, also in New York. Yet somehow the plane they left from is already in Los Angeles before the train leaves the station. How did the plane get from New York to Los Angeles that quickly?