Cole's watch reads 9:30 before he walks around a corner, and 8:55 after.
When James Cole returns from his first trip to the past and is in his cell, he no longer has the bloody wound on his head that he received from his scuffle with the police in 1990. However, when he is being debriefed by the scientists in the next scene, the head wound is back.
When Doctor Railly is spraying the message about the virus on the Animal rights activists place of operations, she clearly is spraying one side of the building, but when they switch to the shot of the graffiti it is on the wrong side.
When Dr. Leland Goines is tied up in the van and blindfolded with the
biohazard ribbon, the ropes he is tied up with disappear and reappear between shots. Also in the final close-up a magnifying glass appears in his jacket pocket. Also the tape moves from his forehead to his hair and back again in every shot
When Cole runs after Dr. Peters in the airport, he is not wearing sunglasses before or when he is shot, but when Kathryn kneels down beside him, he is briefly seen wearing a pair of dulled, brown glasses.
The scene in the department store with the tall indoor glass ceilings (shown both in "good" shape and later "ruined"), occurs in the Grand Court at the old Wanamakers store. In later November, the court would have been fully decorated for Christmas, including the traditional light show, which fully takes up one whole wall of the court. This scene was clearly shot beyond the Christmas season.
The television in the sanitarium announces that the featured
picture is the Marx Brothers' Monkey Business (1931), but the clip they show is from their first film, believed to have been removed, and replaced with; The Cocoanuts (1929).
When Cole is lying under the Land Rover outside the party for Dr. Goines, the front license plate is from Pennsylvania. Pennsylvania has not used front license plates in over 30-40 years.
The scientists of the future should already have had Cole's last message from the airport before they sent him. They played back Dr. Railly's message "before" she had left it in the chronology of the movie, so they could also have had from the beginning all messages that anyone would leave on the secret machine at any time. However, the scientists explain that the process is very time consuming ("one word at a time") and that they had only deciphered Dr. Railly's message a few days ago, so they might not have gotten Cole's message yet.
When they are in the car in 1996 and Cole wishes for the volume to be turned up, Kathryn presses the button on the radio. The frequency changes, but the volume goes up.
-- Actually the frequency doesn't change. Initially time was displayed (9:33) and when she presses the button frequency is displayed (103.7).
A caged hamster is placed in Cole's decontamination chamber, presumably as a canary to check if Cole has contracted a disease that would kill the hamster. But the disease he's trying to bring back only kills humans - it's a major plot point that it doesn't affect other animals.
Correction: Terry Gilliam stated in the making of 12 Monkeys, that he often puts random things in the background of movie scenes, where their meaning or purpose is entirely ambiguous and left up to the viewer to wonder about.
While the unexplained hamster in the scene could be considered a plot hole, it was a deliberate one made by the filmmaker. A plot hole is only a 'goof' if it is an unintentional mistake/
Correction: Terry Gilliam stated in the making of 12 Monkeys, that he often puts random things in the background of movie scenes, where their meaning or purpose is entirely ambiguous and left up to the viewer to wonder about.
While the unexplained hamster in the scene could be considered a plot hole, it was a deliberate one made by the filmmaker. A plot hole is only a 'goof' if it is an unintentional mistake/
When in the car in 1996 and Cole asks for more music, the switching from station to station is the sound of an analog radio dial (fade out of one station, fade in to the next), whereas the radio being used is a digital direct-tune type. This is likely intentional on the part of the filmmakers as Terry Gilliam frequently places "retro" technology alongside or inside the modern.
The belief that the bullet could not be dated from world war I because it is new, is apparently based on a misunderstanding over the method of dating. It wouldn't have been dated using a technique like carbon-14 because it's not organic, so it doesn't matter that it came from the past by time traveling, it is still a type of projectile consistent with those of the period of the first world war.
In the first surface scene, the bear shot is reversed and, thus, it manages to completely inhale the condensation of its breath.
When Kathryn is driving the stolen Jaguar, she goes through a long curve in the road - as seen through the rear window - but she does not turn the steering wheel accordingly.
When Cole meets Jose at the airport, Jose's glasses are shiny; later, while both characters are on the stairs, the glasses are dull in order not to reflect the equipment.
When Dr. Railly is tied to the bed in the motel, her bonds are clearly not very secure. In her struggles, she very nearly frees her right foot, by accident.
When James and Kathryn are in the stolen car driving on the highway, the shadows on the car and the reflections in its windows don't match with the blue screened background.
A major scene is set in and outside the John Wanamaker department store in Philadelphia, with the sign prominently visible. Between the time the movie was filmed in early 1995 and released that Christmas, John Wanamaker was renamed Hecht's, the name it still carried when the events of the film are actually set, in late 1996.
In one scene at the psychiatric hospital in 1990, one of the guards is reading a newspaper from the Weekly World News, a tabloid which published mostly fictional "news" stories in the United States from 1979 to 2007, known for its outlandish cover stories often based on supernatural or paranormal themes. The copy the guard is reading includes the character "Bat Boy", who made his first appearance in the tabloid in 1992, two years after the time settled in the movie.
When Cole finds the Twelve Monkeys symbol on a wall in 1996, Railly dismisses them as marks. Cole runs to her, shouting "Hey!" but his mouth isn't moving in sync with his shouts.
Near the beginning of the film, Cole collects a cockroach as it crawls through the snow. Cockroaches aren't active in winter, and wouldn't be found crawling through snow. Also, the cockroach he picks up is a Madagascar hissing cockroach, not found in the US.
The spider James Cole eats is a Golden Orb Weaver or Banana Spider (Nephila Clavipes). However, that spider inhabits southern regions of the US (mainly Florida), and would never be found in cities in a northern climate like Boston.
It is unlikely, that anybody took a photograph of a wounded soldier in World War I trenches during a combat, especially in night conditions, when photographers had to use flash powder at that time.
If Cole was accidentally sent to World War I era (1914-1918), and got shot in a leg, it is impossible, that he lived on in the past until 1996, especially that he had a fresh wound. There is no mention in the film, that he was recalled and sent back to 1996 again. If so, it is strange, that his wound was not healed and a bullet removed in his present.
Jeffrey Goines credits the Austrian-Hungarian physician Semmelweis for discovering the utility of hand-washing, which is correct. He also names Semmelweis as a proponent of the germ theory, which is incorrect: Louis Pasteur's experiments weren't until the last few years of Semmelweis' death. Goines also mispronounces Semmelweis' name; the "w" should be pronounced like an English "v."
Dr. Railly quotes the Book of Revelation in her lecture, but incorrectly calls it "Revelations".
The bullet "was fired some time prior to 1920" but there is no way that could have been determined unless Jim had somehow limped around with it in his leg for 70+ years. The bullet being an antique is presumably possible to determine but not this, and no need for anyone to "revise or amplify" their statement.