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. 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.
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.
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.
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.
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.
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.
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.
In Professor Umbridge's first class, she gives them all books, then proceeds to tell the class what to expect. During her speech, several of the students's books - particularly Ron's - switch positions from being examined by the students to being flat on the desk. The position of the books repeatedly switches positions as the camera angles switch.
When Mr. & Mrs. Dursley put Dudley into the car to take him to hospital, the hanging basket near the door has mostly white flowers. Later that same evening when they prepare to take flight, they are now red, not white.
During the scene where Harry meets Ron and Hermione at the headquarters, Hermoine's hair changes position. In the first shot Hermione's hair is behind her left shoulder, and in the next it is in front.
In the veil room in the Department of Mysteries, when Harry tells the others to get behind him, we see Ginny stand directly behind Harry with Ron to her right. In the next shot when the Death Eaters arrive and swarm over them, Ron and Ginny have swapped positions in the formation.
In the exchange of presents at the Pheonix Headquarters, Mrs. Weasley is handing over two presents to Fred and George. Firstly, the red parcel is in her right hand and the green parcel is in her left. In the next shot, they are in the other hands.
In the scene when Harry has to write lines for Umbridge, you clearly see him put his hand on the desk, then when the shot changes to a front view his hand is down by his side, and then when it changes back it is on the table again.
When Harry and Mr. Weasley are trying to operate the ticket turnstile Harry pulls their tickets out of his jacket pocket once. Then when the camera angle changes Harry can be seen pulling out their tickets a second time.
During Umbridge's first lesson she uses her wand to write out the OWL acronym on the chalkboard. In the initial shot the three words take up the majority of the board. However, in the shots following, the words are considerably smaller and further to the right.
When Harry and Mr. Weasley go to the London Underground, as Mr. Weasley approaches a turnstile, a man in a brown coat carrying a newspaper swipes his ticket and passes through the gates of an adjacent turnstile. Then the shot changes, and the man with the newspaper passes through the gate again.
When Harry and friends are riding in a cart from the Hogwarts Express station to Hogwarts, in a shot from behind, Luna Lovegood's head is facing to her left. In the following reverse angle, her head is facing to her right.
In the veil room, when the Death Eaters have all but Harry at wand-point, Bellatrix is shown first holding Hermione hostage. Immediately in the next shot she is being held by a male Death Eater, and Bellatrix is shown later to be holding Neville at Wand-Point.
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.
In Ms. Umbridge's potions lesson the camera pans out over the classroom after she has said something and there is the sound of a pencil being dropped on the floor, when students at Hogwarts only use quills. However, this could simply be a dropped wand, as this is the sound we hear when this happens elsewhere in the movie.
In The Goblet of Fire, 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 Jnr. and Bellatrix Lestrange.
After Hermione rings the bell on the bicycle handle, they pan to Grawp and he is now holding the bicycle handle and rings the bell. We never see Hermione give it back, or Grawp take it back. However, if you look closely, they are different handles.
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.
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.
When Harry sees the 'horses' dragging the carriages, the others cannot see him. Luna then claims that he can only see him because he has seen death (Cedric, as he could not see them in previous years). Harry did in fact see his mother die, as shown in a flashback in the Philosopher's Stone, and in a scene in the Deathly Hallows. Therefore he should have seen them all the time he has been at the school.
Lucius Malfoy is a known supporter of Voldemort.
He must have been seen by Harry on the graveyard when V got "resurrected".
Harry and Arthur Weasley see him talking to Cornelius Fudge in the Ministry, but don't say anything?
When Harry and Mr. Weasley are entering the phone box which leads to the Ministry of Magic, at the end of the street several pedestrians are already crossing the road, while the traffic lights for the street are green in the beginning, and switch to red later.
When Harry has the vision of Voldemort torturing Sirius, he is wearing his school uniform. However, when he, Ron, and Hermione are in Umbridge's office to use her fire, presumably minutes after, they are all wearing Muggle clothes.
During the final Battle in the Department of Mysteries, in the shot swooping over the battle, where Bellatrix Lestrange is heard laughing, you see Moody in the bottom right of the shot, and he is clearly dueling with two Death Eaters, but in the next shot a single Death Eater runs out of the rocks, and attacks Moody, yet Moody is not engaged with any other Death Eaters.