(at around 1h 2 mins) When Harry is under the invisibility cloak and throwing snowballs at Malfoy and his cronies, there is a point at which he pulls down the pants of Crabbe and kicks him. In the next shot, Crabbe who was previously on the ground is now standing up, perfectly fine, while Goyle is on the ground in the position of the first. In addition, when the view changes to a long shot, you can see one person being spun around by their scarf and another getting his hat pulled over his eyes, which would be impossible for one person to do on their own.
(at around 1h 30 mins) When Harry uses Expelliarmus on Snape, Snape goes flying into a poster bed which crashes down around him. In a later shot, the bed is again intact, with Snape lying on it, unconscious.
(at around 1h 25 mins) In the hut, when the rock comes flying in the window, it breaks the urn into three large pieces. When we see it broken again later (at around 1h 50 mins), it breaks into several small pieces.
Hermione's hair length grows back and forth all along the movie, often between chronologically adjacent scenes, in a manner not consistent enough to suppose that she gets haircuts.
(at around 35 mins) When Harry is bowing to the hippogriff, his tie is done up wrong - the thin part is much longer than the front part. But when he is riding the hippogriff his tie is done up properly.
When Harry and Hermione go back in time, despite the warning not to be seen by others, they pass in front of the Executioner, just like they did the first time.
(at around 1h 29 mins) While being swung around on a branch of the Whomping Willow, Hermione reaches out one hand, grabs Harry by the front of the shirt and lifts him up. That would require an impossible amount of strength especially for a 14 year old girl.
(at around 2h 20 mins) In the closing credits, "Book of Monsters Repair Shop" is misspelled "Book of Monster's."
After the Quidditch match where Harry falls off his original broom and we hear Fred and George's voices over a black screen as Harry is in the hospital, one of the Weasley twins states he fell over 100 feet. We clearly saw just before Dumbledore saved Harry that he easily fell hundreds of metres.
In the night-bus scene at the beginning of the movie, the bus slams on its brakes to not hit the lady crossing the street. The talking head counts down as the lady crosses, but he counts incorrectly. "...five, four, three, three and a half, two and three-quarters..." The order should be "...five, four, three and a half, three, two and three-quarters."
The Marauder's Map clearly reads "Mooney" rather than the correct spelling which is, as J.K. Rowling spells it "Moony." This was done deliberately as an in joke, as the film's visual effects supervisor is named Karl Mooney.
(at around 44 mins) After the class has finished dealing with the boggart, Harry's scar appears to be on the wrong side. We are seeing his reflection in the mirror on the door of the wardrobe that holds the boggart.
There is no way that the entire Defence Against the Dark Arts class except for Hermione would not know what a werewolf is. Even most Muggle children know what a werewolf is. Snape didn't ask what a werewolf is, but how it differs from an Animagus.
The portion of the Harry Potter and the Chamber of Secrets novel in which Harry gets a warning from the Ministry regarding the Hover Charm Dobby used to throw the cake on the Dursleys' guests did not make it to the film, yet in this film Vernon is still aware that Harry is not permitted to practise magic outside of Hogwarts. However, Petunia should've been aware of this rule from Lily's time at Hogwarts, which could explain it.
(at around 21 mins) When the Dementor attacks Harry on the Hogwarts Express, everything freezes in ice. The bottle on the table does not expand like freezing liquid would. (Only water expands when it is frozen. If the liquid is alcohol of some sort, it will shrink when frozen if it is strong enough. Or maybe there is a spell on it; there are a number of possible explanations for this.)
(at around 43 mins) During the boggart scene in the front view of Parvati, Harry is played by a stand-in.
(at around 1h 2 mins) While Harry (hiding under the Invisibility Cloak) is attacking Malfoy and company in Hogsmeade, he leaves no footprints behind in the snow. However, in all other Hogsmeade scenes, Harry leaves footprints in the snow.
When Harry takes the lollipop from Neville while hiding under his Invisibility Cloak, the part of the stick that his hand is holding should also be invisible, since his hand was still covered by the cloak.
(at around 1 min) In the opening scene in Harry's bedroom, it can be seen in one shot that Harry is lying on a sheet of glass (to allow magical lighting effect) rather than on a sheet.
(at around 48 mins) When the Fat Lady is missing from the picture, and Dumbledore is coming to examine it, Filch is close behind him. As they approach the painting, you can see Filch's cat (Mrs. Norris) with her real green eyes, instead of the red eyes the cat is supposed to have in the movie.
At the beginning of the film Harry leaves the Dursleys and sets off down Privet Drive with his school trunk. Privet Drive in this instance looks nothing like it does in the rest of the series, both before and after this film. It is always shown as a street with endless suburban houses that all look identical (to highlight how mundane Harry's life is when he isn't at school). However, here the street is full of houses of different shapes and sizes.
When Harry and Hermione go back in time , Hermione takes off the time turner necklace and puts it in her shirt pocket , but when they return to the present time , it's still around her neck .
When Trelawney has her moment of clairvoyance before the executioner scene, there's a shot where her mouth doesn't line up with the words she's saying.
(at around 1h 20 mins) When Hermione angrily knocks over the crystal ball during the last Divination scene, a red and black tube can be seen jutting out of its side.
(at around 2h 5 mins) When Lupin is packing up his office, as the camera pans you can clearly see the Boom in the reflection of the glass cabinet.
You can sometimes see lighting devices reflected in the characters' glasses. As Harry is telling Hagrid "It'll be fine" as they are hurrying out the door, you can see lighting equipment reflected in Harry's glasses. Also, in Trelawney's first class, you can see similar lighting equipment reflected in her glasses.
(at around 1h 50 mins) When Harry is bowing to Buckbeak in the pumpkin patch near the end of the movie, you can see the bulge of his microphone battery pack, which is under the back of his sweatshirt.
(at around 47 mins) When Lupin is talking to Harry about Harry's parents a piece of lighting equipment is reflected in Harry's glasses.
(at around 12 mins) The Knight bus squeezes between two buses on Lambeth bridge while traveling North towards the Leaky Cauldron. The other two buses are heading South but one of them has Kings Cross as a destination which is North of the river and is therefore traveling in the wrong direction.
In one shot, there is a white and black butterfly flying, a species that doesn't live in Britain. It's a tropical butterfly, not a cold dwelling butterfly.
When the Knight Bus arrives to the Leaky Cauldron and Harry leaves, it is announced the next stop is Knockturn Alley. Knockturn Alley is less than five minutes walk from the Leaky Cauldron.
Underage wizards are not allowed to use magic away from school, yet at the start of the film, Harry is using the 'Lumos' spell to light up his wand and do his homework, something which would have seen him expelled according to this rule.
The movie adaptation left out the backstory of the Marauders. Therefore, it is never explained how Remus Lupin, a seemingly random teacher (in the book a Marauder under the nickname Moony) knows the passwords to use the Marauder's Map.
Harry would not be able to throw snow balls at Malfoy who was looking in Harry's direction without his arm briefly coming out of his invisibility cloak and this does not occur.
If a Boggart can only be repelled by using the Riddikulus charm, no matter what form the Boggart takes, then Harry's Patronus charm should not have worked on the Dementor-shaped Boggart he practices on.
Nobody explains who the marauders are to Harry, but in later films he refers to Peter Pettigrew as Wormtail and Sirius Black as Padfoot.
(at around 45 mins) When Harry asks Professor Lupin why he didn't allow him to have a chance with the Boggart, Lupin says that he was afraid that it would turn into Voldemort in front of everyone. But the Boggart had already turned into a Dementor before Lupin jumped in front of Harry to redirect the creature at him.
When Professor Lupin is teaching Harry about the Dementor Boggart he's using the Patronus. However, the Boggart is in the form of a Dementor, it's not an actual Dementor and should be treated as a Boggart to be defeated, like the rest of the students did, not using a Patronus.
When the class is on the staircase, immediately before the Fat Lady's disappearance from her picture is discovered, Devon Murray (Seamus Finnegan) can be seen looking directly at the camera for several seconds.
When Harry is in Fudge's office, Fudge is dictating a letter to Uncle Vernon about Aunt Marge. He says, "Dear Mr. Potter" instead of "Dear Mr. Dursley."
Sirius asks Lupin before his transformation "Have you taken your potion tonight?", despite being in Azkaban for 12 years and unknowing that Lupin started taking the Wolfsbane Potion at the start of the school year to be able to teach at Hogwarts.