Continuity mistake: In the last scene on the roof when Holly Hunter shoots the serial killer, he falls backwards. The gun is in his left hand and the path is next to his left hand. The camera then goes to the rear of Sigourney as she walks toward Holly. Only now the serial killer is on the other side of the path and the left hand holding the gun is no longer next to the path.
Plot hole: When Connick has Hudson hanging in the toilets at the start of the movie he grabs the first cop who tries to help her and says he cannot decide whether he should shoot or stab the cop, choosing eventually to do both. At the end of the movie, the copycat does this as well but he makes a mistake: after grabbing Hunter he tells Hudson about not being able to decide if he should shoot or stab but the copycat already had a dead cop's body placed in the toilet in the exact the same way Connick dropped the cop. This makes Hunter the second cop. For somebody with such an eye for detail, the copycat should have done the 'can't decide' monologue with the first cop in front of Hudson, but he is already dead on the floor when she wakes up.