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.
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.
Mills gets out of a bed with only a quilted mattress cover. He puts on his shirt and tie and walks back to the bed which now has a sheet on it.
When Somerset exits the car at the final location, he sees and comments upon a dead dog positioned at the right side of the road ahead of the car. In at least two subsequent scenes, that same stretch of road is clearly visible, yet the dog has vanished.
The phone on Detective Mills' desk changes several times when he enters his new office.
The note Somerset finds behind the refrigerator contains a quote which he attributes to Milton when he presents it to his captain - "Long is the way and hard that leads out of hell to the light". While it's mentioned in Paradise Lost, the quote is originally from Virgil's The Aeneid. It begins with the more famous aphorism that "The road to hell is easy".
Prescription for the sleeping pill says, "Take one cap for sleep. Seconal 15 mg". Seconal only comes in 100 mg capsules and the insomnia treatment is one 100 mg capsule as needed at night.
When Somerset is in the library making copies, a plan of Dante Alighieri's Purgatory comes out of the copy machine, but the label at the bottom of the page identifies it as Dante's Inferno.
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."
While Mills and Somerset are in the police station getting ready for their final confrontation with John Doe, you can see that Detective Mills places the revolver in his holster, and Somerset takes the automatic, but Mills pulls out an automatic to shoot Doe, and Somerset can be seen with a revolver when Doe is shot.
EDIT: When both weapons are being loaded, you can see Mills' bandaged hand loading the magazine into the automatic. Then both of Somerset's hands are shown spinning the cylinder on the revolver. What might have caused the confusion is that when Mills takes his hand off the grip, it appears that the automatic has simulated bone grips, which is more common on revolvers.
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 been secretly thanking me for that one".
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 police are inspecting the body of the "Lust" victim, she is blinking at the beginning of the scene.
The dead "Gluttony" victim can be seen breathing.
In the wide shot of Mills and John after Somerset opens the box, you can clearly see that the person kneeling is not Kevin Spacey.
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 goes to the Mills' apartment for dinner, Detective Mills says that the real estate agent only let them view the apartment for five minutes at a time [because of the vibrations caused by the subway]. Somerset is there long enough for Mrs Mills to finish cooking, and for them all to finish eating the meal, before the subway train goes through - there would not have been such a large gap between trains on a subway line.
When Somerset is talking with Mills: the word ''attrition'' is wrong (in movie including chapter name, and screenplay) - attrition means process of wearing down, as in war of attrition - concerning sorrow for sin, the word is Contrition.
John Doe's journals according to Somerset are ''2000 notebooks, 250 pages each'' - and he estimates it would take 50 men, 24 hrs./day, 2 months to go through them all - how could John Doe have possibly written such an amount? - and considering that writing, especially in this case, John Doe's laborious style, is more time-consuming than reading?
When Det. Somerset knocks on the door of the suspect, the sound of the knocking doesn't match the movements of his hand.
When 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, the camera dolly reflection is visible at the bottom of the two-way mirror.
The story takes place in a city that's rainy all the time yet the city is also surrounded by a desert that clearly doesn't see much rain which doesn't make sense.
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?
Although the film's location is never specified, there is no way a city where it seems to rain almost constantly would be located next to an arid desert.
As the helicopter approaches the high-line towers one of the occupants comments that there's no chance of an ambush because there's nothing there. In fact, there is at least a trailer and a junk car that could easily conceal someone planning an ambush.
No detective with Somerset's experience (or even a rookie) would open or even TOUCH a strange package, especially from a confessed killer, with the Bomb Squad still on their way, just to satisfy curiosity. If the box contained a bomb or anthrax/other toxins, Somerset would've wound up dead or disfigured for no reason.
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.