When the Crow stands at his dead girlfriends grave, the stone angel cries blood. The blood is at first all the way down the cheek, but in the next shot, the blood is just below the eye, and it has apparently dried out.
When Alex is about to drop the cigarette lighter onto the ground to light the gas after the car accident. In the corner you can see someone light it before the flames start up. The light in on the other side of the dripping from where Alex is dropping the cigarette lighter.
Alex Corvis still has a full head of hair when he is being placed in the electric chair. Normally electrocution victims have their heads shaved this helps to insure a proper connection also so that if anything should go wrong their heads won't catch fire.
The U.S. flag hanging in the captain's office is not hanging in accordance with U.S. Army regulations. When the flag is hanging downward, the union (blue field with white stars) is supposed to be facing toward the left, not the right.
The goof item below may give away important plot points.
When Erin shoots the Captain in the ear at the end of the movie, she fires one round and then the gun clicks several times as she pulls the trigger. With that firearm, the Beretta 92F, the slide would be held open after the final round was fired to facilitate reloading. Had there been only "one round in the chamber" as the captain said, the trigger would not have clicked like it did because the slide would have been locked to the rear.