Plot hole: The movie establishes that the FBI has a list of suspects thanks to security camera footage from the area where the victims were found. "A red headed man, two African Americans above average height, a white haired man." Then, the zinger; "a man in his 30s with a tattoo of a rabbit or an animal on his right arm", which of course is our guy Josh Hartnett. We see the tattoo, and it's a little doodle of a sheep, about a couple square inches big, below his wrist. That doesn't really make sense; if they have security footage with that level of detail, one wonders how could the rest be so vague. The next entry mentions "a male with a scar on his jaw", which is even more absurd. Either the security cameras picked those details up along with the suspect's full appearance and mugshot, or they just can't know with such certainty (if the suspect was masked or concealed in any way, then they would know for sure it was the killer and wouldn't be chasing people with wildly different appearances).
Plot hole: After the first murder in Pam's dorm room there should be blood everywhere but when Pam returns to change her dress there is only a single stripe of it on the bedsheets.
Plot hole: The Thorwalds were supposed to be in the apartment for only six months according to the lease, their phone number wouldn't have been published in the phone book for such a short lease.
Plot hole: If the vacuum is strong enough to suck up a hand grenade, why isn't it sucking up the ampules?
Plot hole: In the beginning, Charlotte insists to Velma that cousin Miriam is coming, but Velma says "She's never answered any of your letters." And Drew says she's not coming. But when Miriam does come, only seconds later, Velma and Drew now act like they were expecting her. Velma says "You nearly beat your telegram. We weren't expecting you till tomorrow." It's like the film has been badly edited, with Miriam's announcement of her arrival ending up on the cutting room floor.
Plot hole: Every ghost that we see in the house looks the way they did when they died, for example the girl from the film's intro is seen without skin on her face, which happened to her before she died. However, in the final scene when we see Simon's ghost joining them, he looks completely normal, when he should have had a throat slit wound and the carved markings on his skin. (01:31:20)
Plot hole: Early in the film, we learn that the former prostitute Annie Crook is married to and has an infant daughter (Alice) with Prince Edward Albert Victor. Secretly outraged, Queen Victoria dispatches various high-ranking operatives to eliminate this potential royal scandal. To that end, Prince Edward Albert Victor is secreted away, and his wife Annie Crook is kidnapped and barbarically lobotomized. We then learn that he baby, Alice (who was fortunately in the care of two other prostitutes at the time of the kidnapping), was sent to live with the parents of Annie Crook, no doubt saving the baby's life. That is the last time we hear of baby Alice until near the end of the film, where we are puzzled to learn that Alice was not sent to live with her grandparents at all, as stated earlier. Rather, the prostitute Mary Kelly took baby Alice away from an orphanage to raise as her own. No explanation is offered for this discrepancy.
Plot hole: The pipe bomb that Maggie uses to kill Freddy is the same one that was found in Spencer's room earlier in the film. It's already been established that Freddy was erasing the people he's been killing from existence, so that pipe bomb wouldn't be there to use on Freddy.
Plot hole: Three gunshots were fired for Kurt and Ram's "double suicide" and almost two minutes pass between shots 2 and 3. Doubtful two police officers could think they shot each other.
Suggested correction: An officer could think that one boy shot the other twice, killing him with the second bullet, before that boy was successful in killing him. The remaining boy would then kill himself. "Shot each other" might be a sloppy description, but basically, Kurt and Ram are both dead. There is a letter - forged by Veronica - which "reveals" that they were a couple. No signs of anyone else being involved. The police consider it a "double suicide" because they believe the letter.
Interesting theory, but I respectfully disagree with your correction. Three gunshots to two dead bodies, each with one bullet wound, would arouse suspicion despite what a letter found at the scene says. If one of the boys killed himself, there would be some evidence to support that such as powder burns around the wound or powder residue on his hands. In fact, a forensic scientist would have performed a GSR test on the hands of the shooters to confirm they did in fact fire the weapons.
Plot hole: When the fat guy throws a boot into the ice-spray room, it freezes and shatters on the ground. You can see the length of the shoelace on the ground as well. The shot cuts to the guy in the shaft, and he pulls up the shoelace to reveal the end encased in ice, while the end is halfway into the ice block. This wouldn't be possible, because the other end of the shoelace had no ice at all, and there's no sign either of it breaking.
Plot hole: Regis could have saved himself a lot of time and solved the case much quicker if he had just verified the entries in Carla Town's day planner with the businesses listed. A few phone calls would have told him the entries were forgeries without going to the technician for help.