In the scene following the second task (when Dumbledore is announcing the standings) you can see Neville with Karkaroff behind him. Karkaroff has his hand on Nevile's shoulder. Not only is Karkaroff from a different school, but he is a Death Eater who knew that Neville's parents were aurors (he implicates their torturers in the Pensieve scene) and would not want to touch him as he would be viewed as a blood traitor.
Harry's godfather Sirius Black is in hiding and using codenames in correspondence. Surprisingly, when Harry sends an owl post to Sirius, he writes Sirius' real name on the envelope rather than a codename.
After Harry climbs out of the lake, Hermione covers him with a towel she was wearing moments before. The shot changes to an overhead shot, and Hermione is wearing the towel again. In the next shot, she is putting it on Harry again.
When the Beauxbatons students enter during the opening feast, Seamus is sitting behind Ron on the near side of the table. After Moody enters and "fixes" the ceiling, he is sitting next to Hermione and Ginny on the far side of the table.
In the scene where Fred asks Ron who he is going with to the dance, when you see the letter being passed to Ron, it has four lines of writing at the top of the page, but when Ron reads it, it has only three lines in the centre of the page. You can also tell that the writing is very different in both shots.
When the names are drawn from the Goblet, one of the Weasley twins appears to be two places at once. When Harry sits down on the risers, there is a Weasley twin sitting down farther on the row. In a long shot, both Weasley twins are sitting together at a table on the other side of the hall.
In the tent where the champions are preparing for the first task, Karkaroff and Krum look around and stand up slowly when the cannon is fired. In the very next shot, they are standing up and away from the center of the shot.
In the scene showing the arrival of the Beauxbatons ladies, the shot of Ron and Harry being overly-excited, Hermione and Ginny are sitting next to each other as they show a little bit of disgust at the boys' reaction to Fleur. In the next shot - after the Beauxbaton ladies move past Harry and Ron, they show Ginny and she is sitting next to another girl - not Hermione.
When Ron makes fun of Eloise Midgen, the close up shot of Midgen shows a white girl on her right, then a black girl. On the full room shot, the white girl vanishes from sight, and the black girl is next to Eloise Midgen.
After Harry falls into Dumbledore's Pensieve, he sits next to him and says "Professor?" Behind him you see two women approach and sit down. The camera angle changes to show someone stick his hand through Harry and shake Dumbledore's hand. You can see the same two women approach again and sit down again.
In the scene during which Headmaster Dumbledore is announcing the arrival of the Beauxbatons and Durmstrang academies, Filch is seen running towards Dumbledore to warn him of the arrivals. In one scene it shows that Filch has run at least 20 feet past Ron and Harry. In the next scene the camera pulls to a closer shot in which it shows Harry and Ron are startled to see Filch *just* run past.
When Moody chases Malfoy around the tree after he is transformed back from a ferret, he sticks his walking stick in the ground and it is tilted. In the next shot, you can see the stick in the background and it is perfectly erect.
During the first lesson Hermione moves between two seats. To start there is one person between her and Seamus, and she isn't at the front, she then moves to the front row and there are two people between her and Seamus, then she moves back to her original seat.
At the beginning of the film, when the caretaker is walking to the big house, the flashlight (torch) is in his left hand. When he gets to the outside steps, he switches it from his right to his left hand.
In the wand connection scene between Harry and Voldemort, Harry raises his left arm to steady his wand. The camera angle switches, and his left arm is still beside him and then he raises his arm again.
As Ron is talking about Viktor Krum one of the Weasly twins takes off the Irish flag he's wearing and throws it over Ron's shoulders, Ron is seen taking it off in one shot and when Ginny makes her comment he's seen removing it a second time.
In the scene where Harry has just seen the memory of the court, and gets back to the "real", Dumbledore is standing next to the Pensieve. He's standing up straight, and when Harry walks towards the Pensieve to look into it, he's not looking at Harry. However, in the next shot (in which Dumbledore's sentence starts with: "You see, Harry..."), Dumbledore leans towards Harry. Also, he's holding his wand in his right hand.
When Harry is in the prefect bathroom, solving clue two, we clearly see that the egg is still open as he pulls his head out of the water. Yet, in the very next shot, when his head is above water, we see the egg closed and no sound coming from it, as it is in all shots after that. He would not have been able to close it from one shot to the next.
During the scenes when Harry is being followed across the roof by the dragon he falls and the close shot shows his broom stuck to the roof of the dormer he is on. However when the shot is seen from the dragons POV the broom is not there. When they return to Harry the broom is now on the roof again.
In the graveyard, after Wormtail puts the bone in the cauldron, he places Voldemort's wand in the left inside pocket of his coat. Later, when Voldemort asks Wormtail for his wand, Wormtail pulls it out of the right inside pocket of his coat.
When Alastor Moody uses the imperius curse on the spider, he moves it from his right to his left, from Parvati's shoulder to Ron's head, but in the next shot, the spider is moving from Moody's left to his right, as if the spider is coming from the left side of the classroom, and not the right.
When he has emerged from the bath water after listening to the egg, Harry is sitting with Myrtle and his hair changes repeatedly between shots, going from completely smooth to having a bit of hair sticking straight out on his right side.
During the Quidditch world cup camp scene, you can see what looks like a Niger flag instead of an Irish one. The two are similar, but the Irish flag has vertical green, white and orange stripes while Niger has horizontal orange, white and green stripes with an emblem. However, at a world cup it is only natural that there are people from several nations, not just the two competing in the final. We can also see an American, a Romanian and a Ugandan flag, amongst others, in that particular scene.
Dumbledore introduces the Bulgarian Sons of Durmstrang "from the North." Bulgaria is far south of England, just above Greece and Turkey, but Durmstrang School is not in Bulgaria. It is in the Arctic Circle, with a diverse clientèle including Bulgarians and Germans.
At the end of Harry Potter and the Prisoner of Azkaban (2004) when Harry gets his Firebolt it is black, but in this film his Firebolt is gold and maroon with handles on them. Considering Gryffindor's colors are gold and maroon, and Harry is on their Quidditch team, it only makes sense that he'd modify it for better performance and appearance in Quidditch matches.
When in the maze, Cedric uses the spell "Expelliarmus" on Victor Krum causing him to fall unconscious, when "Stupefy" is the usual charm one would use for that. However, these spells are similar enough to confuse devout Potter fans, and this scene is accurate to the book.
When Harry opens up the Golden Egg in the Gryffindor common room, you can clearly see the Patil twins in the crowd. However, in the book, Padma Patil is not in Gryffindor, she's in Ravenclaw. As stated in the trivia section, they changed Padma to being in Gryffindor instead of Ravenclaw. The twins are shown multiple times in the movie as going places together, and saying things in unison.
When watching the arrival of the Beauxbatons contingent (a stagecoach pulled by seven winged horses), the Hogwarts students are looking in different directions. Some are still looking at the sky, some looking down, others looking straight to the front/camera.
During the scenes in which Barty Crouch Sr. is explaining the rules of entering the Tournament and Dumbledore is subsequently yelling for silence, there are a few shots where you can see that Alan Rickman's, Predrag Bjelac's and Frances de la Tour's stand-ins/doubles are being used.
In the scene where Fred and George are attempting to put their names into the Goblet of Fire, they are talking to Hermione. One of the twins clearly tries to say his line early and is cut off by the other one continuing to talk.
(at around 1 min) In some scenes, there is no glass in Harry's glasses. One example is: the scene where Harry and Hermione are talking on the bridge, near the end of the scene, there is clearly no glass in Harry's glasses.
In the great hall when Hagrid stabs the choir director with the fork you can clearly see that his eyes look over the choir director's head, this is because of scaling issues Robbie Coltrane's reaction as Hagrid had to be filmed on a blue screen and then later added into the frame. Robbie Coltrane was probably looking at a misplaced marker.
When "Mad-Eye" Moody tells Finnegan to not put gum under the desk, he chucks the chalk at him but it bounces off the table behind him and into the girl sitting there before cutting away, suggesting the chalk was rubber.
Part of the incantation used to return Voldemort to power is "Bone of the father, unwillingly given". It would make more sense to be "unknowingly given," as it says in the book, as someone who is deceased cannot give something unwillingly or otherwise. (Interestingly, this goof is actually corrected in some of the dubbed versions, like Swedish and German, where the words in this part are directly lifted from the novel.)
At the cemetery, when Harry is trapped at the statue, Voldemort raises his right arm and places his finger on Harry's head. While Voldemort's arm remains raised his sleeve slides down towards his shoulder, but is back up at his elbow in the close-up.
During the post-cemetery sequence where the crowd is reacting to Cedric's death, Neville appears to be in two places at once. He is given a close-up reaction shot towards the end of the scene, and he is standing between two students. In the shot directly preceding this however, he can be seen on the far right edge of the screen; an unidentified female student is on his left, and she disappears from in the next shot (his close-up).
When Dumbledore is comforting Harry after he has returned from the graveyard, McGonagall can be seen putting her hand on Harry's shoulder, but the very next scene shows her standing far away, next to Snape, as Fudge tries to keep Cedric's death quiet.
At the end of the movie in his address to the students, Dumbledore says that Cedric Diggory was murdered by Lord Voldemort. In fact, Wormtail was the one who killed Diggory at Voldemort's orders. Voldemort was still in such a form that he could not raise a wand. However, Dumbledore's words in the movie are an accurate repeat of those in the book. Dumbledore was speaking figuratively; a literalist would say that Diggory was killed at Lord Voldemort's command.