Continuity mistake: When Lt. Snyder breaks the phone booth window with his gun and points it at Hooker, Hooker's hat falls off. Yet in the next shot over Lt. Snyder's shoulder you can see that Hooker's hat is back on his head.
Continuity mistake: When Hooker meets Gondorff for the first time, he puts him in a shower, fully dressed. When the camera cuts to a front view of Gondorff, as the shot goes back and forth between him and Hooker, Gondorff's right pant leg alternates between being soaking wet and completely dry several times.
Continuity mistake: When Lt. Snyder meets with Polk, the FBI agent, they both sit down and Snyder makes a comment about Polk's "nice office," which is really an empty factory. Polk gets offended immediately and from an over-the-shoulder shot you can see him rise from his chair. The camera switches to a shot of his face and he's calmly sitting down again, then rises up in anger. He stands up twice.