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 up Dante Alighieri's inferno printout, a mistake in the roman numerals can be seen. The lustful, following V. The greedy, should be listed as the 6th (VI) and the gluttonous as the 7th (VII) on the list. However, they're listed as the 7th (VII) and as the 6th (VI) respectively.
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.
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 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.
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.
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.
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?
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.
The goof items below may give away important plot points.
In the scene taking place in the car heading out to find the final two victims, the grating in the vehicle changes. It is more curvy when the camera is on John Doe, while it is very straight when the camera is looking at Mills from John Doe's point of view. It also disappears occasionally, such as then the camera is on Somerset or when it is on Mills, but not from John Doe's point of view.
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.
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.