Early in the film, Pierce wears sunglasses in which the camera operator's reflection is visible throughout the scene.
In the Xavier's hotel seizure scene, when Logan struggles to get back to the room killing off the mercenaries standing in his way, the mercenaries should drop down the moment they are killed (at least those stabbed in their heads), since their minds can no longer be affected by Xavier's abilities. Instead they remain paralyzed until prof. Xavier receives his injection.
During Xavier's seizure in the hotel, everyone is frozen in place by the assault. As Logan passes by the slot machines, one lady is looking around unaffected by the paralysis.
The lat/lon coordinates are in fact North Dakota, just south of the Canadian border, but it is an area that is flat as far as the eye can see, not the cliffs that we see in the movie.
At the farmer's house after dinner, Charles addresses Logan as "Logan" although he had introduced himself to the family as "James." No one seems to notice.
There are no coniferous forests in North Dakota, especially along the North Dakota and Canada border. The terrain in that area is mostly deciduous forests or grasslands.
At the beginning where Logan, Charles and Laura flee from Pierce the first time in their car, the roof window of Logan's car changes its state from open to close in several shots.
Logan and Charles are in the limo going to pick up Laura who is fighting Pierce's men and the police. As Logan is steering the car, there is a very brief shot of the backseat, and Laura is already sitting there.
The video on Gabrielle's mobile is quite nicely edited and narrated for supposedly being a series of underhand recordings. The voice over even extends over several scenes. Being on the run, Gabrielle would hardly have time to do this - even if she had the skill, equipment and software to do it.
Towards the end of the movie Logan shoots Dr Rice with the gun in his extended right hand. In the next cut the gun is in his left extended hand.
In the RAM truck, the antenna of a Motorola production walkie talkie can be seen near the center console. This is very common for communicating with actors during driving scenes.
At the final scene with Laura and Logan, one shot of Laura shows a tear rolling down her right cheek. The next shot her cheek is dry, and she has a dribble of snot from her nose. Then a third shot has the wet tear line back on her cheek and her nose is dry.
When Pierce comes to talk to Logan after returning from finding Gabriela murdered, Pierce reaches his mechanical hand forward and places it on Logan's shoulder. In the reflection of his sunglasses you can see his real hand wearing the green screen glove, at 28 minutes 47 seconds .
In the fight scene at the end of the film during one shot of Logan running, his metal claws jerk up and down slightly out of place as his feet hit the ground, revealing that they are actually special effects appliances held in Hugh Jackman's hands and not fixed blades that extend from the character's skeleton.
When the kids are being chased in the woods by the Reavers, Laura can be heard shouting: "Corred!" ("Run!"). This is how it's said in Spain (from where Dafne Keen learned to speak it), but since her character was raised in Mexico, she should have said "Corran!".
In at least one shot, Gabriela's dead body is seen breathing. (A medium shot from the front)
Logan's entire skeleton is made of adamantium, the hardest metal in the known universe which can only be damaged on a molecular level. Despite Logan's failing healing factor, he still could not have been impaled in the way that he was, due to his adamantium skeleton.
When Logan escapes the smelting mill, the tires of the limo squeal as if on asphalt, but the ground is dirt.
When Logan attacks the mercs who are trying to capture Charles Xavier, he clearly drives his claws through their brains. SInce Charles power over them is based his telepathy, the destruction of their brains (or even serious damage caused to them) should have caused them to collapse as there was nothing left for Charles to control.
In the initial fight scene, Logan gets shot with a shotgun. Although shot at with a gun, no additional wounds appear. Later, he is seen squeezing out bullets in the sink. Shotguns fire pellets, not bullets.
During the first meeting between Logan and Pierce in Logan's Chrysler, Pierce leans in and says "I know what you're hiding, amigo," but his mouth doesn't move.
As the robbers in the opening fight scene run away toward their van you can see Logan's claws fade away rather than going back into his knuckles. This happens at 03:18 in the film.
The movie is in 2029, the only vehicle that is showing as futuristic is the Chrysler 300C limo, all the other vehicles are of 2017. The cell phones would even be different.
During the opening scene where the men are attempting to steal the wheels from the limousine, we can hear the distinctive sound of an air-driven impact driver, as used in commercial tire shops. When we see the outside shot of the man actually removing the lug nuts, he is seen using a standard 4-way lug wrench, and no air tools or air lines are anywhere to be seen.
When Xavier tells Laura that Shane (the Western they're watching on the hotel TV) is nearly a hundred years that is not quite true. As that movie came out in 1953, it would only be seventy-six-years old in 2029. Hence, the phrase "...almost eighty years old" would be more accurate.
In the first gun fight with Laura, the assault rifles have massive muzzle flash's despite being equipped with sound suppressors which not only suppress sound but also contain the muzzle flash.
Caliban likens his weakness to sunlight to the character of Nosferatu. However, in the film Nosferatu there is no character by that name; the vampire's name was actually "Count Orlok," with Nosferatu being his species. However this was intentional as the general audience will not know who "Count Orlock" is but will know that Nosferatu has to relate with Vampires. This would explain why Caliban burns when exposed to sunlight like a Vampire which Nosferatu also means.
Despite being set more than a decade and a half into the future, clothing fashions resemble those of the 2010s. So do the hair styles and the foot wear.
When the main characters are attacked in the casino hotel in Oklahoma City, Logan uses the elevator to return to their room to administer Prof. X's medicine. When Logan gets off the elevator the down button is clearly pressed but nobody is waiting in the hallway to get on.
The price of the X-Men comic book was 40 cents, placing its publication to around 1979. But the comic books in the movie starred the "real-life" X-Men, including Wolverine, who didn't come into the public scene till 2000.
When Professor Charles Xavier was killed by X-24, Laura aka X-23 was supposed to know he is not the real Logan Wolverine by the body smell difference of the two person.
When Xavier falls out of his wheelchair, Patrick Stewart braces himself as he impacts the floor in a way that shows the actor is not really disabled.
When Pierce enters Logan's Chrysler, there was a lady visible through the windshield walking towards Logan's car. The scene focusses on Pierce in the backseat and after some time focusses on Logan in the driver's seat again. The same lady was seen at the same place at the same direction.
When Logan picks the Professor up in the Munsons' house Xavier is facing right but as he carries him up the stairs he is facing left.
In Logan's limo, Pierce presents his business card in his left hand. In the next scene the business card is in his right hand, due to camera angles.