When Nicollette interviews Eddie, he says "...whether it's evidence is yet to be determined", but in a news video playback of the same scene later on he says, "...whether it's evidence or not, we're not sure. We'll determine that later".
The bandage on Jordy's hand jumps back and forth between being neatly fastened and slightly unraveled between shots as he paces in his apartment. In one shot the bandage actually disappears completely, as he raises his hand to finish a drink, we can see the injured hand without a bandage. In the next scene, the bandage re-appears.
When Jordy first saw Daphne she had her hair down and was wearing a collared blouse, but when he gave the description she was drawn with a ponytail with a blue holder, and straps on bare shoulders. When we next see Daphne she is wearing exactly what she was in the drawing, even though no one had yet seen her in that outfit.
When Eddie is talking to Jordy in the burned-down crime scene, his cigar disappears between shots. It is possible that Eddie has taken the cigar out of his mouth off-screen, but it would have had to happen very quickly.
At the beginning of the film, Robert Hawkins (Kelsey Grammer) is in a high-rise building (across from Times Square in NYC) talking to a woman sitting at a desk. They show him talking and the left side of his belt is on the outside of his coat. In the next shot his belt is back under his coat.
Detective Leon Jackson wears a Detective badge (referred to as a shield on the NYPD) but wears a white uniform shirt and Captain's bars on this collar and shoulders. There is no rank of "Detective Captain" in the NYPD.
Emil says that he will fake insanity and have himself declared unfit for trial. This, he says, will result in his being committed to a psychiatric institution where he will miraculously recover and be protected from further trial by the "double jeopardy" laws. While his being "unfit for trial" would, indeed, prevent him from being tried, meaning that "double jeopardy" wouldn't apply, we can, perhaps, excuse his incomplete grasp of the subtleties of foreign law and language, and accept that his plan would work if he stood trial and was declared "not guilty by reason of insanity".