(at around 33 mins) When the young Professor X goes back to his room after rejecting Wolverine's request for help, it shows his room littered with alcohol bottles, as well as a picture of Raven (in human form), with an ash tray with a rolled joint in it sitting slightly behind it to the right (but in plain view). The camera then cuts to a close up of Raven's picture, but this time there is nothing behind it, the night stand had been cleared off for the close up.
(at around 1h 29 mins) When Jornada nas Estrelas (1966) is playing in the background, the episode playing is The Naked Time (1966). At first we hear a comment that the chronometer is going backwards, then were hear the discussion regarding the intermix formula being only theoretical. In the episode broadcast these events happened in the opposite order.
(at around 1h 27 mins) The 747-400 jetliner shown briefly before the 1973 airport scene has the blue, orange and gold livery of Singapore Airlines on the body but with the Pan-Am logo on the tail.
(at around 46 mins) Xavier is talking to Magneto - all the time the first door they came in to the kitchen by has remained open and there is nothing to be seen. Seconds later the door is closed and as the guards enter there is now a stack of colored crates stacked against the wall in the corridor behind them.
(at around 50 mins) During the scene on the Gulfstream (the private jet) between Xavier and Lehnsherr, the collar of Michael Fassbender's shirt and his cravat/scarf are shown in two different positions, alternating back and forth, as if footage from two takes were edited together.
(at around 39 mins) In Quicksilver's first scene, he plays the video game Pong (1972) on an arcade machine. The game is running incredibly fast for showing how fast Peter can play. "Pong" however does not run that fast, and the fact that Peter can move fast would not make the game run any quicker.
The story in 1973 takes place over the course of some ten days or so in January and includes scenes in Paris and Washington, DC. These locations are normally rather cold in January, but the scenes set in those cities indicate a milder temperature. (For example, no one ever wears any winter clothing.)
When young Charles Xavier and Erik Lehnsherr played chess on the plane they start playing with black, but In Chess rules white always start the game.
Major Stryker is shown wearing Silver Star and Meritorious Service ribbons with "V" devices for valor. The V device is not awarded with the Silver Star or The Meritorious Service Medal.
(at around 1h 45 mins) Richard Nixon and his entourage enter the bunker through the Oval Office, however when Magneto extracts the metal bunker, it emerges from the Main Residence. The Oval Office isn't in the main residence, but in the West Wing. This is a common misconception about the residence.
(at around 1h 30 mins) When the Pentagon is shown, the caption says "Washington, DC." though the technical location of The Pentagon is Arlington, Virginia. However, it has been insisted by many that the building is not just close physically, but is very linked to Washington's political and economic culture, that the employees generally think of themselves more as 'Washingtonian' than 'Virginian'. Additionally, at least two official seals (one's in the Pentagon press room) state 'Washington' (or 'Washington DC') at the bottom making the identification not entirely wrong.
(at around 47 mins) Quicksilver uses a portable music player in 1973, while the Walkman wasn't invented until 1979. He is using a stolen prototype of a device called a "Stereobelt", which was first tested in 1972. The prop used in the film is an accurate replica of the historical device. The headphones he is wearing are of a style (individual earpieces which clip directly to each ear) which was not commercially available in 1973, but could have easily been created by removing the headband from headphones of that era and attaching small pieces of metal or plastic.
The entire idea of there being anachronisms in this film is a goof in itself. Since this is an alternate universe with multiple examples of advanced technology, along with events that never occurred in our reality, virtually any "anachronism" can be explained by non-parallel development. Maybe Pink Floyd debuted for the Christmas shoppers. Stark or Trask may have advanced the armor and arms for 'Nam. If any parallel realities exist, MP3s might have been obsolete by 1980. Everything is theoretically possible.
The entire movie is about trying to stop Trask from acquiring Mystique's blood, and giving the Sentinels the ability to adapt to resist mutant powers. Because Mystique can only imitate the appearance, and sometimes voice, of someone else, it would initially seem like Rogue would be more useful in this. But her power is more about draining the target, while Mystique is all about mimic/adapt to whatever she wants; a perfect base power for a weapon against a variety of unknown powers when combined with transmuting abilities.
Paris police are shown collecting a swab of Raven's blood off the ground, and Erik warns her that humans will use "your blood, your genes to create a weapon that wipes us all out." In 1973, only one gene had ever been sequenced, a microscopic protein the previous year. The best analysis available in 1973 could determine only blood type, and the amount of blood on a cotton swab would have been too small even for that. The ability to analyze DNA evidence is strictly a 21st-century development. However at the moment that Magneto said that, he had already interacted with a Wolverine from the future, and talked to him during a very long flight from America to Europe. Explaining why Magneto would know about something that had not been discovered yet.
(at around 49 mins) The newspaper that Wolverine prevents Magneto from picking up has the headline "Peace Treaty to be signed in Paris". The article then proceeds to describe the Paris Peace Accords of 1973 in the past tense.
When Magneto is on top of the train carrying the Sentinel prototype, his hair and clothing should be blowing wildly due to the speed the train is moving. However, neither are, revealing it to be a greenscreen special effect.
The newspaper that Wolverine prevents Magneto from picking up in the airplane has an article about the Peace Treaty, which contains several repeated paragraphs about a shoemaker.
Most of the film takes place in January 1973 during the Paris Peace Accords, with scenes set in Paris, New York, and Washington DC. In the film, it is springtime with fully bloomed trees and characters wearing warm weather clothing, when it would have been in the dead of winter.
(at around 1h 25 mins) When Magneto is on the train he sends rails into the train car to takeover the Sentinels. He is doing this from the top of the train. The Sentinels were not originally made of metal so how does he see where they are? He would be able to sense the train cars but not the Sentinels inside.
(around 1h 4 mins) When Beast and Erik fight near and in the fountain, supposedly in Paris, a monumental column dedicated to Admiral Nelson can be seen clearly in the background in few shots.
The serum that Hank gives to Charles is derived from his original mutant-gene-suppressing formula. So while it may suppress Charles' mutation (telepathic powers), it cannot give him the ability to walk as that disability was caused by a physical injury to his spine and is not a result of his mutation.
When Charles, Hank, and Logan go down to use Cerebro, Hank says Charles hasn't used Cerebro since he first went looking for students. While there is a layer of dust on the Cerebro helmet and console, the bridge to the console and the corridor look as though they've been freshly cleaned.
(at around 44 mins) When helping Charles Xavier and Wolverine free Magneto at the Pentagon, Peter Maximoff is seen wearing a Dark Side Of The Moon t-shirt. Magneto is being freed prior to the X-Men travelling to the Paris Peace Accords that took place in January 1973, but the Pink Floyd album wasn't released until March of that year.
(at around 1h 35 mins) When Magneto levitates RFK Stadium, it seen with a baseball diamond and configuration. In 1973 RFK Stadium was not being used as a baseball venue as the Washington Senators had moved to Texas following the 1971 season.
A 747-400 jetliner can be seen in a 1973 scene. This variant of the 747 did not fly until 1988.
(at around 47 mins) Quicksilver used modern ear-hook style headphones, which were not available in the seventies.
(at around 1h 1 min) Mystique is shot with a taser in Jan 1973, but the first taser was not around until 1974.
Despite DNA sampling not being available for analyse to the extent shown in 1973, had Magneto managed to kill Mystique in the room, instead of the bullet hitting her in the leg as she jumped from a window, her blood and brain tissue would have been spread around the room allowing Trask to collect everything he needed to create the Super Sentinels.
Erik tells Charles he tried to save JFK because he was 'one of us' - a mutant. This comes as a complete surprise to Charles, even though he has the tools to detect any mutant on the planet, and has often used Cerebro to search for them. Erik, on the other hand, has no such ability.
When Mystique reveals herself in the conference room and Stryker is pointing his gun at her there is a clear line of sight yet he still does not shoot her. Mindless goons who try to grab her don't interfere with the line of sight as he is aiming across the table.
(at around 2h) The Washington Sentinel newspaper article about finding Magneto refers to a state of panic in the "neighbourhoods" of D.C. An American newspaper would not use the British/Canadian spelling of "neighborhood."
(at around 22 mins) When "Colonel Sanders" enters the barracks in Vietnam, the barracks is called to attention. The soldiers rise and go to the position of Parade Rest (feet apart, hands behind their back). The position of Attention is feet together, hands at their sides.
(at around 32 mins) When Logan asks Xavier for his help in 1973, Xavier says that Logan said 'Fuck off' when they asked him for help in X-Men: Primeira Classe (2011), this is not true, Logan says 'Go Fuck yourself' when Xavier and Erik approach him in the bar.
Xavier deduces that Magneto was involved in the Kennedy assassination because the bullet curved. Not only is this impossible, nobody claims that it did. Those who doubt the "single bullet theory" often refer to it as the "magic bullet theory," because they believe the bullet would have had to change direction several times to cause all of the injuries to both Kennedy and Governor Connally. In fact, the positions of their bodies in their seats, and of the seats in the car, created a straight trajectory for a single bullet.
After Brian Cox as W. Stryker in X-Men 2 (2003) (and here in a flashback scene), who is 172 cm tall (5' 7½") they cast Josh Helman who is 16 cm taller (188 cm i.e. 6' 2"). At least he is as tall as Danny Huston who portrayed Stryker in X-Men Origens: Wolverine (2009).