(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.
(at around 1h 17 mins) When they were loading the Sentinel onto the train, there was a shot of a military guard with an M16. His helmet was of a modern PASGT style, not the style used in 1973, which would have been the Vietnam era M1 model.
(at around 49 mins) The film is set in 1973, but the private jet with tail number N540EA is a 1975 Gulfstream II. Actually, it is a Gulfstream IIB, which was not approved by FAA until 1981 and uses the Gulfstream III wing (see the winglets) which was not available until 1979. The original Gulfstream II was introduced in 1966.
(at around 39 mins) The 1973 events of the film are implied to take place in January, as this is when the peace accords in the film were actually held. When Quicksilver is first visited in his basement, he is listening to "Hello Hooray" by Alice Cooper, from the album "Billion Dollar Babies". Billion Dollar Babies was not released until the latter days of February 1973.
(at around 2h) The Washington Sentinel newspaper article about the reconstruction of RFK stadium mentions the Mayor of Washington. Washington, D.C. would not obtain a home rule government and a locally elected mayor until 1974, a year after the events of the film.
(at around 1h 45 mins) The purple seats in the lower ring of the upper deck of RFK Stadium were installed in the early 1990s. In 1973, these seats were light blue. Also, the 400s only go as high at 471, there is no section 482.
(at around 41 mins) When they were touring the Pentagon it was obviously daylight outside. Yet, when the security monitors were taken over they said it was regular television feed. In fact, they were showing Sanford and Son. This can't be since in 1973 this would have been the second year it was on television. And thus, would only be on at night and not syndicated.
We occasionally see Paris event scenes shown as if bits of newsreel or shot by one of the TV cameras. However, these are in a modern 16:9 screen format rather than the more squarish 4:3 format of 1970s TVs.
(at around 1h 35 mins) Though the movie is set in 1973, When Magneto flies in RFK Stadium over the cityscape of Washington DC, he looks at a Washington National Cathedral with a completed west end (not finished until 1976) and the scaffolding on the central tower to stabilize the damage from the 2011 earthquake.
(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 'F*** off' when they asked him for help in X: First Class, this is not true, Logan says 'Go F*** yourself' when Xavier and Erik confront him in the bar.
(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 Star Trek is playing in the background, the episode playing is Star Trek: The Naked Time. 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 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 42 mins) After accessing the last entrance of Magneto's cell, Quicksilver bends down to slide in non-metallic food plate. Here, in this shot we can clearly spot a metal watch buckled over his wrist. In the next shot it disappears.
(at around 1h 9 mins) When Raven is hit by the bullet after diving out of the special meeting room she is struck in the leg on the inside of her right calf. Later in the French hospital we see the bloody gauze and bandage on the outside of her right calf, however Erik pulled the bullet out of her leg and so there was no exit wound on the outside to require a bandage there or to cause bleeding.
(at around 46 mins) In the Pentagon Kitchen - as the door opens, two guards, both in full uniform, enter the kitchen, but a third guard (with no security jacket) appears from the side of the screen, as if he had just entered with the other two.
As the previous two guards, who were knocked out by Wolverine, were both wearing jackets, it couldn't have been either of them. Also, a fourth (no jacket) guard appears, in front of the two jacket-wearing guards, though no other guards were seen to enter the room.
(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 44 mins) When Quicksilver is breaking Magneto out of the Pentagon, after breaking the glass they wait for the door to open, as soon as it does they burst through the hallway to the elevator sending all the guards crashing to the ground, but when it shows them in the elevator you can briefly see back down the hallway to the door they came from but all the guards are missing. Also when it shows them go through the hallway it is solid white, but the shot from the elevator shows a black and white striped hallway.
(at around 47 mins) When Quicksilver uses his powers to deflect bullets and cause mayhem while getting Magneto out of prison, the early parts or the scene showing Wolverine's claws extending clearly show the glint and shape of his adamantium claws. This film is set before the experiment that coats his bones in adamantium, and the bone claws are clearly feature not only earlier in the film, but later in this scene as well as later in the film.
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.)
(at around 47 mins) As Quicksilver begins making his loop around the kitchen, he puts on his headphones and listens to over a minute of 'Time In A Bottle'. He is moving many times the speed of sound as evidenced by the fact that the bullets only move a few feet. That means the music would have barely begun coming out of his headphones by the time he was done.
(at around 39 mins) In Quicksilver's first scene, he plays the video game Pong 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.
(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.
(at around 1h 11 mins) When Magneto and Mystique met in the French subway, Victor Hugo station, we can see that it's a kind of a big hub, in the reality, this station is located in a district where very few people use it, even fewer in 1973.
(at around 43 mins) It's confirmed that there is no metal inside the Pentagon where Magneto is being held (otherwise he would be able to use it to escape), however, when Quicksilver breaks the glass the concrete door's close automatically as a security measure, and even though the doors are concrete It would be impossible to achieve that sort of security measure without the use of metal mechanics and electronics (which all have tiny metal parts.)
(at around 23 mins) The date written at the top of Alex Summers' classified military lab report from Trask Industries is written in the European day-month-year format (as 21/01/73) instead of the American month-day-year format. Since it's an American military report, it should be in the latter format.
(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.
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 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.
(at around 55 mins) Eric is being held underneath the Pentagon for supposedly assassinating JFK. He later claims he was attempting to save him because he was fellow mutant but failed. Magneto has never had a problem deflecting or even stopping bullets mid-flight as an old man or youth as evidenced in the first X-Men and in X: First Class.
The entire movie is about trying to stop Trask from acquiring Mystique's blood, and giving the Sentinels the ability to use mutant powers. However, Mystique can only imitate the appearance, and sometimes voice, of someone else. They would have to get Rogue's ability instead as she absorbs and obtains other mutants' powers.
(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.