Somerset states in the film that there are "7 cardinal virtues, and 7 deadly sins". It is generally more accepted, and stated by Saint Thomas Aquinas, that there are only 4 cardinal virtues, the other 3 virtues being theological.
At about the end of the library scene, when Somerset is folding a print of Dante's Purgatory, a mistake in the roman numerals can be seen. The lustful and the gluttonous, although in proper roman numeral order, need to be swapped around on the list.
When Somerset is in the taxi on the way to the library, he is wearing a striped shirt under his overcoat. When he gets to the library and is chatting with the security guards he is wearing just a solid white shirt.
When the detectives are at the door of John Doe's apartment, John walks into the hallway. He sees them, drops his bag of groceries, pulls a gun, shoots, and runs. The bag is now on the floor, with its contents spilled out. When Mills gives chase, he runs down the same hallway. The dropped bag of groceries has vanished.
The layout of John Doe's apartment conflicts with the hallway of the building. In the outside hallway, there is a window looking onto the building next door. Inside the apartment, there are rooms where the window would be.
The level of the wine glasses when Somerset is over for dinner changes. When the camera is on the Mills, Mrs. Mills glass is higher than Somerset's glass. When the camera is on Somerset, the levels are both lower and equal.
When Somerset is in the greed victim's office dusting the wall for prints behind the painting, he does so with his left hand. However, the close-up shot of the hand doing the dusting is clearly a right hand.
As Mills and Somerset are driving to the Sloth victim's apartment, it's clear that the scene in the car was shot on two separate occasions, with the first half of the drive on one day, and the second half on another day. Brad Pitt's side burns change significantly from thicker with a pointed edge, to a bit shorter without a point and somewhat thinner. Also the seat belt next to Pitt changes position with the buckle insert visible in the first half, then completely gone in the second. Other little difference's are Pitt's white shirt collar, and the brim of Freeman's hat.
The photo Detective Mills finds of himself and Somerset, which was taken by John Doe, does not correlate with any of the three pictures that Doe actually takes at the crime scene. As we can see in the film, Mills was never in the position that's depicted in the actual photograph.
At the end of the scene where both witnesses of the "Lust" crime scene are interrogated, there is a slow track from one interrogation room to the other. In the tracking shot, you can see the camera dolly reflection at the bottom of the two-way mirror.
When Somerset returns to the Gluttony crime scene, he uses his pocket-knife to cut the police tape which is securing the door. This tape is on the inside of the door, which is pointless (as it is supposed to be seen by people, to warn them away from the crime scene) and impossible, unless the police taped up the door and then climbed out of the windows.
Many fans and critics initially thought the movie was clearly set in New York City, so the nearby desert was seen as a geographical error. In fact, while the story was inspired by screenwriter Andrew Kevin Walker's unhappy time living in Queens, the film explicitly does not take place in NYC or any other specific locale; in this manner, the desert being so close to a major metropolitan area is not a mistake.
There are at least 3 copies of Dante Alighieri's Divine Comedy which Somerset places on the table. The red-bound copy which is the focus of an earlier shot is seen underneath a copy of Geoffrey Chaucer's The Canterbury Tales. Beneath the red one is a larger printing of the book with a dust-jacket, and at the top of the other pile is a smaller, blue-covered version of the book.
John Doe killed the defense attorney Eli Gould for immoral and unethical professional practices yet retains his own lawyer to become an accomplice to blackmail Mills and Somerset to complete his "masterpiece". In actual fact, the reason he killed Eli Gould was his notoriety as both a greedy man and defending know guilty parties (and thus letting them go free and not having to pay for their crimes). This is evident in the car ride where John states to Mills and Somerset "I know you must have secretly thanking me for that one".
When they remove the painting which is supposedly placed upside down, the picture frame's string to hold the artwork against the wall is fixed two thirds up so that it could not have hung the other way without hanging far away from the wall. This means, that with the frame's string position it could only hang the way it is seen in the film and not the other way. Hence the comment that "he moved the screws to rehang it."
When Jon Doe turns himself in to the police he is covered in blood from that is said to be from killing the "pride" victim, and detective mills' wife. When he gets to the police station, the blood is still somewhat fresh. The delivery man that brings the package with the head in it said that Jon gave him the package and told him to bring it to the destination at 7:00 exactly. This means that Jon would have to had been covered in blood when he gave the box to the delivery man sometime in between killing the two women and turning himself in. I highly doubt the delivery man would have taken the package from a man covered in blood, and it is highly unlikely that Jon cleaned himself off, gave the package to the delivery man, then went back to both victims and covered himself in blood.
When the detectives find the fingerprints that say "Help me" behind the painting and submit them to be found in the database, the technician says that it can take up to three days to make a match. Later they talk about how they found Sloth in the apartment exactly a year "to the day" after the first photo of him was taken. If the killer wanted them to find Sloth on a particular day, how could he have known how long it would take the police to find a fingerprint match?
John Doe murders Tracy Mills, mails her head to her husband, and then turns him in to her husband immediately after, still covered in her blood, which resulted from the murder scene. This means that he would have had to go to the delivery man--who tells Somerset that he was hired to deliver the package--covered in Tracy's blood, and looking like he just killed someone, without arousing any suspicion.
The SWAT team enters Victor's apartment to arrest him, and they don't appear to see "sloth" written on the wall behind his bed until they discover that he is "dead." Even with all of the air fresheners hanging on the ceiling, they should have seen the word "sloth" written on the wall as soon as they turned to face the bed, and called for Mills and Somerset then.
When Detective David Mills is chasing the suspected murderer (who is now on the roof top in between buildings), he fires shots at the Detective in the building. Nearby pigeons can be seen only a few feet away and do not fly off when the shots are fired.
As Mills and Somerset leave the Captain's office after submitting the report on their first job together, Somerset walks across the screen to leave the room. In the bottom-left side of the screen, the red marker tape he is standing on is clearly visible in the shot.
When Somerset returns to gluttony's apartment he cuts a police "keep out" sign to let him in. This sign is on the inside of the apartment when it should be on the outside of the door. It would be impossible for this sign to be placed on the inside unless someone remained in the apartment.
While Somerset and Mills are driving in what appears to be a torrential downpour, the parked cars seen outside Mills window look dry, as do the streets and sidewalks. Sunlight can be seen in some shots also, which wouldn't happen in such a severe deluge.
The goof items below may give away important plot points.
When Mills orders Jon Doe to the ground in the police station, Jon Doe is covered in blood but doesn't leave any blood on the floor, even though the police officer who handcuffs him gets blood on himself.
When Somerset and Mills are driving John Doe to the final crime scene, the grating between the front and back seats of the car appears and disappears in various shots depending on the camera angle. At some camera angles it would not be visible, but it is missing from some shots where it should be visible.
At the "Sloth" murder scene, John Doe has amputated the victim's hand in order to leave fingerprints at other murder scenes. When the police examine the victim, tied to his bed, the handless, prosthetic left arm built from the scene is visible, as well as the actor's real (and intact) left arm, strapped to the side of his body.
When the delivery man at the end of the film hands over the box that contains the head, he clearly hands over a light weight box. A human head is quite heavy enough that it would have involved some effort to lift.
Just before the greed scene, several newspaper headlines state that Defense Attorney Eli Gould had been murdered. Hence, Mills and Somerset refer to him as "the biggest defense lawyer in town." (Casual viewers might have misread the headlines.)
When we first see the crime scene for lust, the man with the large leather strap-on device has a white sheet draped over him to cover the obviously disturbing contraption. Even though it was recently used to stab the female to death through intercourse and should be covered in blood, there are no soaked through blood stains on the sheet.