Errors in geography: Hudson Hawk is being pulled along the Brooklyn Bridge by an ambulance. When he breaks free from the ambulance, he exits the bridge in the left lane. He ends up at the toll plaza for the Brooklyn Battery tunnel, which is about three miles away.
Factual errors: Hudson Hawk is given a brick of gold and a brick of lead while blindfolded to demonstrate that they are indistinguishable by weight. Gold is 70% more dense than lead and the weight difference of those bricks would be easily noticed. A gold brick of that size would weigh about 30 pounds, but they handle it as if it weighs a couple of pounds. It is also mentioned that gold and lead differ by one proton on the periodic table of elements, but they differ by 3 protons (and about 7 neutrons).
Continuity: At least one of the objects on the table in the Five-Tone Bar disappears suddenly, shortly after the coffee machine breaks down.
Continuity: The packing beans that are stuck to Hudson Hawk's face when he gets out of the crate move around and change shape
Continuity: As Hudson is speaking with Anna on the couch, her dress jumps back onto her shoulder between shots.
Continuity: After injecting Hawk's leg, the syringe the Almond Joy removes is just as full as when she started.
Revealing mistakes: When Tommy and Eddie jump from the museum/auction house, the cables attached to their stuntmen were visible for a second.
Continuity: When the Mario Brothers are chasing Hudson Hawk in the ambulance on the Brooklyn Bridge, the air fresheners hanging from the rearview mirror and the needles hanging from Antony Mario's face change.
Factual errors: Actor Carmine Zozzora has his name misspelled Zozorra in the closing credits (it's correct in the opening credits).
Factual errors: Eddie, who knows these things, says that the song "Xanadu" is 4 minutes 19 seconds. The song's playtime is 3 minutes 27 seconds.
Errors made by characters (possibly deliberate errors by the filmmakers): When Tommy is quizzing Hudson Hawk on song lengths, he asks "National Anthem, Whitney Houston - Super Bowl 17"? Whitney Houston sang the National Anthem at Super Bowl 25, not 17. Leslie Easterbrook (Callahan from the Police Academy movies) sang the National Anthem at Super Bowl 17.
Audio/visual unsynchronized: As Hawk is riding the gurney behind the ambulance, the plastic IV bag on the gurney gets shot, and the sound of shattering glass is heard, as if the bag were an old-fashioned glass bottle. In a subsequent shot, the IV bag is intact again.
Factual errors: Several characters in the film are paralyzed using curare, but remain able to breathe, talk and move their heads. In reality, poisoning with curare results in paralysis of the muscles necessary for breathing (in addition to the others) - and subsequently death.