(at around 30 mins) When Harry, Hermione, Ron and Neville are in the carriage with Luna her hair is curly, yet in the next scene (what would be shortly after) her hair is completely straight.
(at around 1h 11 mins) In one of Harry's Occlumency lessons with Professor Snape, the window behind Harry has long vertical bars. When the camera pans out of the room, those bars are not there.
(at around 34 mins) When Harry is asleep during his first night at Hogwarts, he is wearing a striped, light blue T-shirt. But when he has a vision of Voldemort and sits up in bed, his shirt is now solid dark blue with buttons.
(at around 3 mins) The design on Dudley's shorts changes inbetween the scene from when he was bullying Harry with his friends, and when Harry and Dudley are in the tunnel with the Dementors.
(at around 4 mins) When Harry is fighting off the Dementors, he produces a patronus and his wand is pointing at the Dementor that attacked him. When the scene cuts to Dudley on the ground, Harry's wand is at his side. When it cuts back to Harry, his wand is pointing at the dementor again.
(at around 1h 13 mins) Phineas Black's name is misspelled "Phineus" on the tapestry at Grimmauld Place.
When Harry is talking to Sirius Black in the waiting room at Kings Cross there is a poster in the background with a Network Rail logo on it. The film takes places in 1995-96, however Network Rail was not founded until 2002.
Near the beginning, when Harry, Dudley and Mrs Figg are walking home shortly after the dementor attack, it is night-time. The ministry's letter states that the attack took place at 6.23pm. However, in August, in Surrey, England, sunset is not until 8pm.
(at around 1h 21 mins) In Harry Potter and the Goblet of Fire (2005), when Harry is looking in the Pensieve, Igor Karkaroff accuses Barty Crouch Jr. of torturing Frank and Alice Longbottom. In The Order of The Phoenix, after a DA meeting, Neville tells Harry it was Bellatrix Lestrange. Both statements are in fact true, as according to the books Frank and Alice Longbottom were tortured by a group of Death Eaters, which included both Barty Crouch Jr. and Bellatrix Lestrange.
Only a few characters can see the Thestrals, but anyone can ride them after being helped to mount them by people that can see them, just as a blind person can ride an ordinary horse. This is how so many students can ride the Thestrals to London.
(at around 37 mins) Umbridge punishes Harry for an outburst where he claims that Voldemort killed Cedric Diggory in the previous film, Harry Potter and the Goblet of Fire (2005). Cedric Diggory was really killed by Peter Pettigrew (Wormtail), but only after a direct order from Lord Voldemort. Voldemort can be said to be analogous to Adolf Hitler (and others alike), who did not personally carry out his killings.
(at around 21 mins) During Harry's trial, Fudge pronounces the name of the court as the "Wizenagamot"; the real name being the "Wizengamot". This could be intentional, to further underline Fudge's incompetence as Minister.
(at around 18 mins) When Harry and Mr Weasley are descending into the Ministry, using the visitors' entrance, only the inside of the phone box in the street moves. When the scene cuts to the interior of the Ministry, they're in a complete phone box. However, if you look closely you can see that there is in fact a frame moving inside the original phone box, clearly it is a double. Otherwise, guests would have been in danger of falling off.
(at around 1h) During the first "D.A." training/meeting, harness and wires are visible as characters are thrown back after being struck by a spell.
(at around 1h) When Nigel blasts Harry backwards, the retraction line pulling him is briefly visible, as is his safety harness.
During the hearing, when Mrs. Figg has just described the dementors, and Fudge starts talking again, there is a close-up of Harry, with no scar.
In multiple shots throughout the movie you can clearly see that Harry's glasses have no lenses in them.
The scars put on Harry's *left* hand by Umbridge's special quill keep switching hands between shots.
Petunia is seen watching the weather on a flat screen TV. The film, like the book, is set in 1995 and flat screen TVs did not appear until the mid to late 2000s.
(at around 18 mins) When Harry is being escorted by Arthur Weasley to his hearing at the Ministry of Magic, the two find themselves in a tube station which contains barriers that one may gain access through by use of an Oyster Card. J.K. Rowling has gone on record to state that Harry was born on July 31st, 1980. This would mean that the fifth installment in the Harry Potter series would take place in 1996, for Harry's fifth year in Hogwarts would see him being 16 years old. As this is the case, Oyster Cards would not exist at this time due to the fact that they were first invented in 2003. This mistake is under the pretence that the Harry Potter universes' time line was the same as the real world's, with the fictitious addition of the magical world.
(at around 31 minutes) in the Gryfindor common room there is music playing in the background. The song is "Boys Will Be Boys" by The Ordinary Boys, which was not released until 2005 but this film is set in 1995 a full 10 years before the song's debut.
At 5 minutes and 13 seconds the Dursley car number plate can be seen. The film takes place in the year 1995, however the number plate style is that of a post 2001 UK number plate, specifically the year 2006.
(at around 1h 45 mins) When Lucius has Harry and company at wandpoint in the Department of Mysteries, Bellatrix Lestrange walks out from behind him. In the audio she is laughing maniacally and talking to Harry, but when you look at her, her mouth is barely moving. She mouths "He knows how to play" a full second after it is heard, and her mouth moves at a much slower pace. She also has a deadpan expression on her face, not the maniacal face you would expect her to have while laughing like that.
(at around 2h 5 mins) Near the end, when Harry and Luna are having a chat, when Luna says '...if not always in the way we expect', she is not moving her lips at all.
When Harry is first looking at the veil in the Department of Mysteries, bars of blueish light connected to either side of the arch are visible.
(at around 1h 45 mins) When Harry and his friends fly on the Thestrals to London, they are coming from Hogwarts, which according to the novels is somewhere in Scotland. So if they are flying from the North of the UK towards Westminster in London, where the Ministry of Magic is located, there is no reason why they would fly over the Canary Wharf district, which is 5 miles east of Westminster, especially if they are in a hurry to save Sirius Black.
When Harry is escorted to Sirius Black's home by broomstick, near the start of the film, he flies upriver from Tower Bridge on the Thames to Westminster Bridge. He is travelling from Little Whinging in Surrey to Islington. Although the exact location of Little Whinging is unclear, a more direct route should have taken him down river and he needn't have been anywhere near Tower Bridge unless they'd taken a VERY circuitous route.
It is known from the previous movie that memories can be extracted and viewed through magic, yet when Harry needs to prove his claims on his Wizengamot hearing, nobody thinks of doing this to Harry's memories of that night, or Dudley's, who, although a Muggle, knows about the magical world. While this was probably deliberate from Fudge, as part of his determination to convict Harry, it makes no sense from Dumbledore, who defends Harry on the trial.
(at around 43 mins) When Harry sees the thestrals dragging the carriages, the others cannot see them. Luna then claims that he can only see them because he has seen death (Cedric, as he could not see them in previous years). Although JK Rowling said that he wouldn't have recalled his mother's death clearly enough because of him being just a baby at the time. he did watch Quirell die before him in Harry Potter and the The Sorcerer's Stone. So he should have been able to see Thestrals since, at the earliest, his second year at Hogwarts.
As Harry trains Dumbledore's Army in the room of requirement, they practise extensively with Expelliarmus spells. This should have resulted in mass chaotic shifts of wand allegiances.
(at around 1h 45 mins) Bellatrix Lestrange has been imprisoned for 14 years, well outside any contact with society, so how does she know (or recognise) Neville Longbottom the second she sees him? He was barely one year old 14 years ago.
During the battle between Voldemort and Dumbledore, their wants engage in priori incantatem. It is established that this is a phenomenon caused by "sibling wands". As Voldemort's wand and Harry's wand are siblings, this would not work between Voldemort's wand and Dumbledore's wand (the Elder Wand).
Neville says that he never performed an Expelliarmus spell before, but in one of the previous Dark Arts trainings (within the sequence where Filch, Draco Malfoy & co. try to enter the Room of Requirement) he clearly performs one.
(at around 1h 26 mins) When Umbridge is holding detention, one of the Weasley twins dips his quill into the ink well, even though no ink is needed for these quills.
(at around 9 mins) Mad-Eye Moody tells Kingsley to take point as they escort Harry to headquarters, but throughout the flight Moody is in the lead. During the flight over the Thames River - just before the ferryboat - Kingsley can be seen to Harry's left. Moody should have told Kingsley to guard their flank.
There is no reason for Mrs. Figg to say last year when she says "after You-Know-Who killed that poor Diggory boy last year...", it happened just a couple of weeks ago.
Despite Harry's previous experience with Dementors, he never thinks to offer Dudley some chocolate at home, especially seeing how angry Aunt Marge and Uncle Vernon are.