(at around 46 mins) After Harry gets sorted into Gryffindor he goes and sits down next to Ron with Hermione across from him who is sitting next to Percy. In the next shot when Harry asks who's that teacher next to Professor Quirrell he asks Percy and Hermione is sitting to the right of him and Ron is across from him.
(at around 17 mins) Dudley eats Harry's birthday cake with his hands, but when he turns around, after Hagrid has given him a pig tail, there is no cake or icing on his hands or face.
Harry's scar clearly changes positions throughout the movie.
(at around 2h 20 mins) During the end of the film, as the train starts leaving Hogwarts, you can see that Hagrid is a little bit taller than the train. In the next camera shot, Hagrid is shorter than the train.
(at around 1h 29 mins) When Harry is in the restricted section, he sets down the lamp to his left before taking off his invisibility cloak, setting the cloak to his right. When Filch's voice is heard and Harry grabs the cloak, the lamp is on top of the cloak and thus falls onto the floor.
(at around 1h 30 mins) When Harry, wearing his Invisibility Cloak, sees Filch looking for him, then spies on Professors Quirrell and Snape arguing, the shots filmed from Harry's point of view have him at eye level with the adults even though he is clearly shorter than they are.
(at around 6 mins) When Harry is at the zoo, the snake clearly blinks. Snakes don't have eyelids.
(At around 1h 6 mins) Wood tells Harry that, if he catches the Golden Snitch "... the game is over" and "...we win." This is only partly true. Catching the Snitch will end the game, but the team with the most points at that time is still the victor, regardless of who catches the Snitch. While the 150 points for catching the Snitch means that the team that catch it usually win, it is possible for the other team to win if they are already leading by more than that amount.
Most, if not all British owl species are nocturnal. Therefore seeing them routinely flying during the day would attract Muggle attention, something the Wizard world always try to avoid.
After Hagrid bends the shotgun Vernon was holding, it blows up a huge hole in the roof. Despite this the heavy rain does not pour through the roof.
Many viewers think that baby Harry Potter is an infant at the beginning of the film (which would make it inconsistent as he is shown to be a toddler in photos with his parents, who were just killed). He was actually a toddler tightly wrapped in blankets. (as the part in this film was entirely played by the Saunders triplets).
(at around 1h 45 mins) In one scene, Hermione calmly says the word "Voldemort" without the customary flinch or shudder. However in all future scenes and sequels, Hermione is clearly reluctant to say the name and does not overcome this fear until Harry Potter and the Order of the Phoenix (2007). However, as Hermione is Muggle-born and is still young, it is possible she does not yet know the full significance of the name.
(at around 50 mins) When Ron and Harry come into Professor McGonagall's class late and she transforms from a cat into a human, she is not wearing glasses at first, yet they appear on her face as she turns to address the boys. This effect is on purpose. She is transforming between cat and human as she approaches the boys and her glasses are the last thing to reappear.
(at around 30 mins) Many viewers believe that the infant Harry in the flashback (set in 1981) is wearing anachronistic Blue's Clues (1996) pajamas. The design on the sleeve is actually a rabbit and not "Blue".
When Wood is showing Harry the Golden Snitch, after it is released for flight he is shown looking elsewhere and not where the Snitch is. Although this might be seen as a mistake, it is actually intended to give the impression that only a Seeker is skilled enough to follow the flight of the Snitch which Wood had described as "Small, wicked fast and damn near impossible to see". While Wood, the Gryffindor teams Keeper is not able to find the flying Snitch, Harry as the team's new Seeker is easily able to see it.
(at around 1h 11 mins) When Harry is upside down with the troll holding him by his legs, his hair is pointing to the floor and his scar is no where to be seen on his forehead.
(at around 9 mins) When Harry receives his first letter, Uncle Vernon says "Yours? Who'd be writing to you?", Dudley is standing next to him and is seen mouthing Uncle Vernon's lines.
(at around 1h 50 mins) As the three children run across the field to Hagrid's hut, Harry says a few lines ending with "... why didn't I see it before?" Hermione is mouthing Harry's lines with him.
(at around 1h 55 mins) In the scene with the flying keys, we can see the string holding up the broomstick just before Harry grabs it.
(at around 54 mins) When Harry is reading aloud the article in the Daily Prophet about the break-in at Gringotts, he reads words that are not in the article. In particular, he says, "The vault in question, Number 713, had in fact been emptied earlier that very same day." The words "Number 713" do not appear on the page. Harry would have then been unable to connect this to the vault he and Hagrid visited at Gringotts.
When Harry comes to the station there are numbers showing the platforms. There are two number 10 and two number 9 platforms on each side of the platforms, with a separation between the pillars. The ticket did not specify which side of the platform to use. Muggles have two different trains with different designations, usually going in different directions/locations.
The Hogwarts scenes are set from 1991 till 1992, one newspaper seen reads 2001 at the top right. (error also acknowledged by the prop designer).
In the first scene when baby Harry is being left on the Dursley's doorstep, there are late 80's an early 90's cars parked in the driveways of the houses on Privet Drive, even though this is supposed to be in 1981, when Harry is one year old.
Right before the Dursleys along with Harry Potter go to the zoo, the car the Dursleys own is a 1999 Vauxhall Vectra. This scene alongside the events of this movie is set in 1991 and the generation shown is a Vectra B which didn't go into production until 1995 and only the Vectra A's were in production and existence the time this movie is set.
(at around 12 mins) When Harry receives countless acceptance letters from Hogwarts, he fights with Uncle Vernon, saying the dialogue "They're my letters! Let go of me!" Harry's voice is far deeper than the Harry in the rest of the movie, indicating this line was re-dubbed long after main production when Daniel Radcliffe's voice had already begun to change. (Also, his lips are not moving when he says those lines.)
Owls are very quiet in flight. They have to be, they are hunters and rely on being able approach their prey silently and hear where that prey is in the first place. The owls in Harry Potter - especially in the scene where hundreds of them gather outside the Dursleys' house in Privet Drive - are very loud. Every time they appear, the soundtrack contains loud flapping noises which sounds more like some sort of pigeon than any owl.
(at around 1h 11 mins) When Harry and Ron are fighting the troll in the girl's toilet, they use a spell to lift the troll's club over its head and drop it. The club does hit the troll and makes an appropriate sound effect, but when the club falls to the floor, it makes no sound at all.
(at around 1h 12 mins) In the scene following the defeat of the troll, Quirrell is shown speaking with the other professors, at which point they, and the trio, leave the girls' bathroom. Their footsteps are clearly heard as they move down the hall; however, in the next shot of the troll laying on the floor, the sound effects have ceased. In the last shot, of Quirrell jumping nervously in response to the troll grunting, the footsteps can again be heard.
(at around 35 mins) Twice in the film, the British word "bogey[s]" is spoken: once when Harry and Ron meet on the train, and once at the end of the troll scene (at around 1h 12 mins). On the American DVD, the subtitles transcribe this as "booger[s]", a synonym which sounds very different.
(at around 1h 3 mins) When Harry, Ron and Hermione just left Fluffy for the first time and walk into their dorm area, we see, under the painting, the feet of someone closing the painting.
(at around 1h 30 mins) When Harry takes Ron to the Mirror of Erised, when Harry drops his cloak and runs away, you can clearly see the lime green from the outside.
(at around 1h 4 mins) The mechanism which makes the Quidditch box shake can be seen underneath the box when Wood falls over after catching the Bludger.
(at around 32 mins) At King's Cross Station, the camera crew is reflected on the left side of the train on the right.
(at around 41 mins) Floating candles hanging from visible wires.
(at around 32 mins) Hogwarts students reach the train by going through King's Cross Station platform no. 9¾, which is secretly located in the barrier between platforms 9 and 10. In reality, platforms 9 and 10 are in separate buildings, and there is no barrier between them, but railway tracks. People wrote to J.K. Rowling about this, and she admitted getting confused between King's Cross and Euston stations. The Platforms actually used in filming are platforms 4 and 5.
(at around 34 mins) Harry and Ron first encounter each other on the platform at King's Cross station, yet on the Hogwarts Express, when Ron asks Harry if he can share his compartment, mountains can be seen out of the windows. This could not be until at least a couple of hours after leaving London. Why did it take Ron so long to find a seat?
(at around 56 mins) When the students are first learning about brooms, Madam Hooch tells the students to kick off from the ground once she sounds her whistle. She blows her whistle and Neville starts to rise from the ground. Even before he loses control of the broom, she yells at him. He's the only one who did as he was told. Why is he in trouble?
Hermione mentions that Alohomora is a first-year level spell. A door with a deadly three-headed dog behind it in a school should have a better lock than what can be opened with such a basic spell.
In the giant game of chess, Ron sits on a black piece, which puts him at risk when the piece is attacked. But the other pieces can move without someone sitting on them, so there was no need for him to sit on the piece.
Hagrid tells it's top secret what he picks up in the Gringotts safe. Firenze however somehow knows the Philosopher's Stone is kept in the school.
During Christmas break, Hermione packs her belongings to spend Christmas with her family. Earlier in the movie, to get from Hogsmeade Station of the Hogwarts Express to the grounds of Hogwarts is to ride on boats across the Great Lake and vice-versa. She would not have been able to sail across the lake during these cold winter months as doing so can be very risky.
(at around 44 mins) In the sorting ceremony scene, Ron goes up to get sorted into his house. After being put into Gryffindor house he runs off in the direction of the tables on the left side of the Hall, even though we know that Gryffindor house table is on the right side.
(at around 48 mins) When Percy is taking the first years to Gryffindor Tower, they all seem excited by the idea of moving pictures, even though most of them would have come from magical families and moving pictures would be perfectly normal to them.
(at around 7 mins) When Dudley falls into the snake pit and the glass reappears, by looking at the expression on his face he is calm so we can tell he thinks that there is no glass. He then puts his hand against the window and then gets scared. If he didn't expect glass he wouldn't have put his hand against the window.
(at around 40 mins) When Harry arrives at Hogwarts, Professor McGonagall announces that the Sorting Ceremony will begin "momentarily". In UK English, momentarily means "for a moment" (i.e. briefly), and a Scottish witch as pedantic and precise as McGonagall would never use the American meaning of the word ("in a moment" or "soon"), even though the American meaning might be well understood. Then again, given that the otherwise equally pedantic Snape says "less" when he means "fewer", it could just be that the teaching staff's use of English is just as sloppy as it is in schools all over the Muggle world.
In the giant game of chess, Hermione stands on a black square, but she should have been on a white one.