As Hawk is riding the gurney behind the ambulance, the plastic IV bag on the gurney gets shot, but you hear glass shattering, as if the bag were an old-fashioned glass bottle. In a subsequent shot, the IV bag is intact again.
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. Leslie Easterbrook, who played Callahan in the "Police Academy" movies, sang the National Anthem at Super Bowl 17. Also the Whitney Houston version was 116 seconds not "7 minutes 17 seconds" as Hudson claims.
When Hudson Hawk is at the Vatican taking notes, the camera shows a left handed person writing. Next the camera shows Hudson Hawk holding the pen in his right hand and the note pad in his left hand in the mirror behind him.
After Hawk is confronted by George Kaplan, his notebook is lifted by the henchwoman. She reads the list of items including 100 stamps. The next scene has Hawk riding the mail train to the Vatican. Ignoring the visible stamps on the side of the carton, there are at least 209 stamps on the top of the same carton.
When Anna is shot by the curare dart, she falls next to Hudson with her right arm on the floor by the side of her leg. In the next shot, her arm has moved up onto the top of her leg. If she was paralyzed, and no one moved her arm...it should still be by her side.
When Hudson Hawk gets out of the crate, the packing peanuts stuck to his face move around and change shape. One of them is behind his ear when he looks out the window at the Coliseum. In the adjoining scene when the Butler says, "Welcome to Rome," Hawk turns around and the Styrofoam piece behind his ear isn't there.
Hudson Hawk is pulled along the Brooklyn Bridge by an ambulance. When he breaks free, 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.
When Eddie and Tommy are in the recorder room of the auction house, Tommy tells Eddie that they have about "5 minutes and change." Eddie says "5:32 - Swinging on a Star." The version of the song that they sing as they are robbing the auction house is (at best) only 2 minutes 36 seconds (less than half of the time for which they have planned).
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% denser than lead, and the weight difference would be easily noticed. The gold brick would weigh about 30 pounds, but they handle it as if it weighs a couple of pounds. They also mention that gold and lead differ by one proton on the periodic table of elements. The difference is actually 3 protons and 7 neutrons.