In the first murder, Eugene fires two rounds into the victim from a revolver, then walks away without ejecting the engraved shell casings later found at the scene.
When the grocery store robber is shot and thrown through the window, it shatters like tempered glass; when Megan looks down at the robber on the ground, broken pane glass is clearly shown.
Wrapping a gun, especially one as powerful as the .44 Magnum, in a towel will hardly dampen the sound of the gunshot. In fact, it's more likely to set the towel on fire due to the enormous muzzle flash.
During the final shootout, Megan fires at least 8 rounds before reloading, while Eugene is never seen to reload despite firing more than a dozen rounds.
When the killer is in the bathroom near the end, he can be seen reloading his pistol with spent ammunition. Spent cases have an indentation in the primer (the round bit in the middle of the back of the case) which are visible in the rounds used.
During the final scene, Megan runs out of ammunition and, having only one working hand, sticks her revolver inside her waistband to reload it. After being fired repeatedly in the space of a couple minutes, the barrel of the gun would be hot enough to severely burn her, even through her clothes.
Megan fires more rounds than her revolver can hold without reloading in the finale subway and street scene.
Megan fails to secure the supermarket robber's gun after shooting him. Of course, this is contrary to the police's protocol, but this is a rookie police officer's first day and she just killed a man. She has no backup, and she's likely in shock. It is easily believable that she might overlook that important step in the process.
When the robber falls through the shop window, the face of the stuntman is visible, and it obviously is not Tom Sizemore.
Moments before the best friend, Tracy, is killed, a blood bag is visible over her heart underneath her clothing.
When Megan is talking with her mother at the police precinct, Megan sips from a paper coffee cup. However, when the light hits the cup, it can be seen to be empty.
When Eugene is working out in his apartment while listening to a news report on the killings, the TV can be seen in the mirror; the reporter's lip movements don't match what she's saying.
When Eugene is pointing the gun at the restroom mirror, the sound of him cocking the hammer is heard, yet the cylinder doesn't rotate.
Megan's suspension hinges on the fact that the robber's gun wasn't found and the main witness, the cashier, provides an unclear statement even though the gun is right in his face. But at least two other people - the old woman in line after him and another male customer were up close during and after the confrontation.
Considering he fires far more than the six bullets the gun had when he stole it, at some point Eugene had to buy ammunition. It never occurs to the cops to inquire at gun shops in the city about recent purchases of .44 Magnum rounds, which would at least give them descriptions of possible suspects if not IDs.
Each time Megan draws her service pistol, she has her finger on the trigger. Police officers are trained to not do this unless they fully intend to shoot, something Megan - a recent academy graduate - should know.
When the detectives find the suspect digging around in the park dirt for his buried gun, they stake out the park by sitting in their car rather than calling in a metal detector to find the gun.
Megan Turner, a recently trained police officer, is twice easily manhandled by the killer. First he holds her from behind with one arm while shooting her friend, and later he sexually assaults her, again holding her down with one arm as his left arm is damaged and bleeding from the gunshot wound.