Lighting in the foyer of the 1845 mansion was provided by light bulbs in a grand chandelier. The first home to have electrical lighting was that of Joseph Swan, one of the inventors of the light bulb, in England in 1879. A mansion deep in the Canadian wilderness would not have been outfitted with electricity until several decades after that.
When Team X infiltrate a compound in Nigeria John Wraith's weapon of choice is a G36K assault rifle with an AG36 grenade launcher, the scene is set in the 1970s and this rifle began introduction in the 1990s.
When Victor and Logan are fighting in the Vietnam War (during the opening credits sequence), Victor ends up getting in a fight with American soldiers many of whom are carrying M-16 rifles with a 20" barrel and full barrel guard as well as a period correct non adjustable butt-stock. However when we see Logan running to help Victor, he is carrying a modern AR-15 style carbine rifle with an adjustable butt-stock and smaller 18" barrel with a round barrel guard which wasn't around during the Vietnam War era.
(at around 52 mins) In the helicopter chase through the forest, when Logan is on the motor bike, you can clearly hear the separation of shots coming from the machine gun mounted on the side of the helicopter. However, it is a Gatling style machine gun capable of shooting 6,000 rounds a minute. The sound of it firing is more like a hum rather than a typical bang-bang-bang sound from a standard hand held sub-machine gun. The sound department appears to have simply chosen a "machine gun" sound from a list without being accurate to what type of machine gun it is.
Weapon XI has single long blades that run through the length of his arms. Since adamantium can't be bent, this would mean when the blades are retracted, Weapon XI can't bend his elbows. Yet in the "activating" scene, his elbow was bent.
(at around 57 mins) When Scott Summers is in Spanish class, we see verb conjugations written on the chalkboard. The words "tu" and "el" are written without an accent mark. So they mean "your" and "the" in Spanish, not the pronouns "you" and "he" respectively.
(at around 48 mins) When Wolverine notices the farmer's motorcycle, he calls it a chopper. It's supposed to be a 1964 Harley Davidson FL, and appears to be in pretty much stock condition. A chopper is a bike that has been stripped down or "chopped" to a bare essentials condition. However, the term "chopper" is incorrectly used by many people to describe any kind of large motorcycle.
(at around 49 mins) When the farmer speaks to Logan the morning after he sleeps in the barn, Logan is sitting sideways on the motorbike, he gets off it and stands up to put the jacket on, but the bike doesn't move at all. Then when he mounts the motorbike again it bounces on its suspension with his weight.
(at around 1h 7 mins) When Gambit is first introduced in the casino, he has a slight beard (especially noticeable when he says "Do I owe you money?"). However, after knocking Wolverine through the wall and into the alley, he is shown to be almost completely clean-shaven.
When Logan and Victor's fight causes them to smash through a window, Logan's hair is a mess from the fall but in the following shot as Logan turns his head, his hair is perfectly combed, followed by the next shot where his hair is once again messy from the fall.
(at around 44 mins) As Wolverine awakens in the adamantium injection tank, several shots in a row shows the diagrams inked all over his body to guide the needles. Seconds later, when he stands up to escape, there are no marks on him anywhere.
(at around 1h 15 mins) After Wolverine jumps from of the plane near Three Mile Island he takes some violent bounces across the water. Yet when he shows up moments later in the facility he is completely dry and his clothes are unscathed.
(at around 54 mins) When Wolverine flies through the air towards the Zero's helicopter you can see the blades of the copter spinning in one direction but when it switches to the close-up as his claws cut the blades, they are spinning the other direction. This may be due to the frame rate of the camera used, similar to when car wheels look like they are spinning backwards when they are filmed.
(at around 51 mins) When Zero's chopper approaches the barn for the first time, the closeup of the rocket pod shows that it is full. The chopper fires one rocket from each pod to destroy the barn. When next we see the chopper it is hovering in front of Logan, trapping him between it and the 2 vehicles. There is a brief glimpse of the rocket pods. Each rocket pod now has 2 rockets missing, when there should only have been one.
In Lagos, while Team X is walking up to the building, only one katana is visibly strapped to Wade's back. Later in the elevator, both are visible, although he did have time to strap it on while walking to the elevator.
When Wade sharpens one of his swords on the plane, he's sharpening a traditional curved Katana. However, when the team arrives in Lagos and he fights his way through the final group of soldiers he's wielding two straight-bladed Katanas.
(at around 11 mins) In Nigeria, Zero throws his guns in the air with the slides shown locked open. In the next shot they are closed as he catches them with new magazines, and begins firing immediately without chambering the first round (which is necessary in order for all semi-automatic pistols to fire).
(at around 44 mins) After Logan breaks out of the adamantium injection chamber and escapes the facility, there's a close up of him looking out into the wilderness. His hair is nicely shaped and dry even though he just came out of a chamber that was filled with water.
(at around 1h 2 mins) When Wolverine knocks out Blob during their fight the ring's ropes collapse under Blob's immense weight. At different points during their conversation following the fight the ropes appear either upright as if nothing had happened or still collapsed.
(at around 1h 1 min) In the boxing match between Wolverine and the Blob, when the Blob is losing his balance his position changes several times from different shots. At first the poster on the wall is behind him then the corner by the wall is behind him, then when he falls backwards on the ropes it is on the open side of the ring towards the room, the opposite side of the poster.
(at around 1h 2 mins) When the Blob falls on the ropes at the end of his boxing round with Wolverine, the ropes are underneath him and one is over him near his neck, but this rope disappears instantly when Wolverine stands over him with his claws in the next shot.
When Victor and Logan are both on the tower fighting Weapon XI, it is clear that the tower side changes when XI begins attacking the 2 brothers. When XI jumps over Victor and Logan, the tower side marks that its on the right side of Victor, but in the next scenes it changes to his left side. Later in the battle scene Victor turns himself to get XI by his neck.
On Zero chasing Logan by a helicopter scene; while two SUV chasing Logan, just after the helicopter appears at the and of the road, you can clearly see that helicopter's rocket launchers are empty. After Logan cuts trough SUV from the side, we see helicopter from behind where rocket launcher has only three blanks on left launcher where at the beginning of scene before blowing up the house they only sent two rockets from left and right launchers.
(at around 15 mins) In the jungle scene where Sabertooth and Wolverine begin to get at odds you can see the fog machines shooting out mist in spurts. At one point you can actually see the pipe and nozzle.
(at around 13 mins) After Wade comes off the elevator near the beginning of the movie, cutting at bullets and clearing the path to a man with diamonds, he stops and stays in a lounging position after cutting down the last two men. In that instance, two wires are clearly visible near his shoulders.
(at around 45 mins) At some point a car drives over a one lane bridge (before the Wolverine goes to the paddock). After the bridge an arrow pointing forward is on the left hand side of the road, revealing its filming locations of Australia and New Zealand. This also shows the old couple driving on the wrong side of the road, even though this was supposedly America.
(at around 1h 14 mins) When Wolverine and Gambit are flying in the plane, they are carrying on a normal conversation but without the use of headsets. In a small, two-seater plane it's nearly impossible to hear your own voice screaming, much less someone next to you, because of the proximity of the engine to the passengers.
Sabretooth and Wolverine are supposed to be brothers, but in the first X-Men movie they encounter each other several times and there is no mention of this connection. This is because Sabretooth suffers from amnesia just like Wolverine, as explained in the comic book "X2 Prequels: Wolverine", which takes place between X-Men and X-Men 2.
(at around 28 mins) Kayla tells Logan the story of a wolverine howling at the moon. Wolverine vocal cords are unable to make a howling sound. But cultural stories are not always scientifically accurate, especially if they are a way for a culture to explain something in nature.
In this film, Scott's optic blasts generate heat as seen by the scorching they leave behind. In the other films (and all other media) Scott's optic blasts only generate concussive force. However, it is said that Dr. Xavier has helped Scott's progress and has helped him to control the intensity of his optic blasts.
(at around 47 mins) As Wolverine is admiring his new claws in the bathroom he touches the tip of one, making a shrill sound as of metal striking metal, though it was only his fingertip, but this is because his fingertip is also made of adamantium, and as seen, Wolverine pokes his claw through his skin, making it possible to make a squealing sound.
The movie opens in "North-West Territories, Canada, 1845". The Northwest Territories (containing what is now the Northwest Territories plus Yukon, Nunavut, Alberta, Saskatchewan, Manitoba, and large parts of Ontario) were not part of Canada until 1870, but this caption is made for a modern audience, who would be unfamiliar with the geopolitics of 1845.
In the bar in Canada when Logan faces Creed, and the close up shots of Logan holding his claws to Creed's face, when Logan exposes and retracts his claws you can see 'wrinkles' of skin between his fingers but when the claws are not moving the skin is smooth. However, these wrinkles could be a result of the damage to Wolverine's skin every time he exposes or retracts his claws. The smooth shots are the result of his healing power recovering from the wound.
(at around 24 mins) Wolverine puts the wrong end of the cigar into his mouth shortly before Zero shoots it, or so it seems. In fact, the head of his cigar is merely raggedly clipped and heavily chewed, and can be seen as such in previous shots.
(at around 44 mins) When Logan escapes from the facility where he got the adamantium fused to his bones, he makes an "X" in the wall, but the middle sections, which ate not connected to anything, do not fall.
When the farmer and his wife arrive in the pickup, the camera switches to a shot on level with their eyes looking through the windshield at them. A supposed reflection appears on the glass in front of them of a naked Wolverine running across the road. But the windshield is sloped back, so a reflection in it would show the sky; not ground level. To see ground level, the camera would have to be above the truck looking down at double the windshield's slope.
The goof items below may give away important plot points.
(at around 1h 35 mins) At the end of the film when Wolverine is talking to Gambit, the links that his dog tags are clipped on with move. In one scene, you can clearly see the link is at the side of his neck, but when it cuts to Gambit and back to Logan, it is hidden.
(at around 1h 30 mins) Sabretooth is clearly being shot through the chest by Weapon XI laser vision, yet when Sabretooth regenerates and stands up there are no holes in his shirt or cape, as if it never happened.
(at around 1h 8 mins) Victor kills John Wraith by sticking his hand into Wraith's torso and ripping his spine out. Later, when Logan sees Wraith dead on the ground, Wraith's shirt is buttoned, clean and intact.
(at around 1h 19 mins) When Kayla Silvertooth "dies", it is said it is due to an injection of hydrochlorothiazide. This is a diuretic drug, all it would do is make her urinate more. It is also not available by injection.
When Wolverine leaves Gambit's plane, he takes off his jacket before jumping out. He doesn't leave the island with Gambit, and therefore never gets his jacket back. But, in X-Men, he still has the jacket. However, with a 17 year gap between this movie and the first X-Men, it's possible he gets his jacket back, but as yet it's not explained how.
When Wolverine discovers Silver Fox during her faked death, she is laying in a pool of blood and her clothes are ripped and bloody, implying that she died at the claws of Sabretooth. Later, they explain that she faked her own death by taking some sort of drug to make her appear chemically dead. If she just took a drug to create the illusion of death, then she didn't need to suffer any real wounds to fake it. However, when Wolverine discovers her body and assumes she's been killed by Sabretooth's claws, wouldn't he have noticed that physically she didn't actually have a wound on her entire body and become suspicious that she actually wasn't dead? Also, Wolverine has an extremely advanced sense of smell. He should have been able to tell she hadn't been freshly killed. Even if it was her blood that had been collected earlier, he should have been able to tell it wasn't fresh. (This could have been done on purpose to illustrate Logan's unfortunate tendency to be blinded by his overwhelming rage. The tremendous level of stress he would have gone through during the entire ordeal would have been staggering. Since he's also not one to sit around and wait he may have left her there and gone off to avenge her. There's the possibility that Sabretooth was very aware of Wolverine's sensory capabilities and knew how to counter them, but they didn't go into it.)
(at around 42 mins) After the operation that Logan undergoes it's shown that he is dead, and in the X-ray you can clearly see his throat moving. However, this could also be seen as a sign that he is still alive, which is confirmed moments later as he emerges from the tank.
(at around 1h 12 mins) Although Jason Stryker appears to be younger than Cyclops in this movie and yet seems older in X-Men 2, it is entirely possible that by the time the events of X2 take place, Jason has been through so much mistreatment at his father's hands that he is prematurely aged.
In the finale, the mutants who will become the first generation of students for Xavier's School are freed by Wolverine. One might expect that the students to mention the grizzled, hairy rescuer with long metal claws in his hands, or that their psychic mentor might pick up on it. Cyclops is the only exception, as he was blind throughout that sequence. Yet when Wolverine reaches Xavier's School in X-Men movie, he is a complete mystery to everybody. However, none of the children saved from the prison become an X-Man with the exception of Scott Summers/Cyclops, who didn't see Logan/Wolverine save the children from the prison.
(at around 54 mins) When Logan destroys the helicopter, while the helicopter is rolling one can clearly see that the cockpit is empty. In the next shot, all of its passengers are back inside. However, if you look closer you can actually see a pair of legs and a torso (attached together) flying near the top right corner of the cockpit, and then when the chopper lies still, the legs are smacked against the cockpit.
When Stryker, and Sabertooth capture Scott in the school Stryker says "All that is left is Logan", but after that in New Orleans Sabertooth is seen taking blood from John Wraith. So Logan wasn't the last one. This may be because Wraith's power may have been considered an extra bonus that could be retrieved if the opportunity arose. Stryker may not have expected to be able to catch Wraith because while he can track and restrain Logan, Wraith can teleport away at any time as long as he is awake. Also, Logan was willing to undergo the procedure (which was secretly a test to see if Deadpool would survive the procedure) because he wanted revenge for Kayla's death, whilst Wraith is ashamed of what he has done with his powers and would not willingly use them to help create a super-weapon.
It is established that Logan was born with healing ability and his bone claws. Later the adamantium he was injected with got bonded to them and the rest of his bones, and became his metal claws. So Weapon XI should have only gotten his healing ability and his bone claws, not adamantium ones. However, Deadpool would have been given the same procedure as Logan, as indicated by the fact that Logan was just a test to see if Deadpool would survive said procedure.