(at around 1h 35 mins) When Seamus tells Dean to get more towels for Harry when he gets out of the lake, Dean runs off, but in the next shot, Dean is still right next to Harry.
(at around 18 mins) 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.
(at around 18 mins) During the opening dinner, Neville switches position at the table from beside Hermione to the other side of the table, next to Dean.
(at around 1h 9 mins) When spying on Neville practicing for the Yule Ball, Harry and Ron's hair is significantly shorter than in the following scene.
(at around 45 mins) When Harry is talking to Sirius through the fire, Ron stumbles in on them talking and says that he heard voices. Harry quickly dismisses this and Ron leaves. The camera then goes to a wide angle shot of the room where you can see Ron walking in an upstairs balcony. From this position, Ron would have clearly been able to see Harry talking into the fire with Sirius, and would have never have had to come down stairs and ask about the voices.
When Harry's name comes out of the Goblet of Fire, the piece of paper it's written on has blue ruled lines on it, typical of normal notebook paper. But the magical schools use rolled parchment, which wouldn't have these lines.
(at around 2h 30 mins) One of the credits is for "Assistant Choroegrapher" (sic).
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.
(at around 1h 3 mins) 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.
At the beginning of the movie, Frank Bryce is listening to the radio and it gives the forecast in degrees Fahrenheit. Taking place in England, the temperature should be given in Celsius. Some British weather reports do in fact give temperatures in both.
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.
(at around 1h 55 mins) 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.
(at around 1h 25 mins) In some scenes, there is no glass in Harry's glasses, such as 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.
(at around 21 mins) When 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.
(at around 1h 30 mins) In the second task, Karkaroff can be seen mouthing the words that Dumbledore is saying.
(at around 1h 40 mins) In the courtroom scene when Karkaroff is first shown, Michael Gambon's body double can be easily seen off to the right.
(at around 19 mins) 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 Harry is in the Prefect's bath, he opens the egg under water but does not put his head in the water to listen. However, when he puts his head in the water, the song is perfectly timed from start to finish for him to hear the entire song.
When the group is going to the Quidditch World Cup, they touch the port key which is an old boot. The boot does not come with them, it disappears. When Harry and Cedric touch the Tri-Wizard's cup it goes with them.
(at around 1h 50 mins) Before the cannon fires for the third task, Amos Diggory can be seen hugging Cedric. He then says "my boy" even though his mouth is seen not moving.
(at around 1h) When the Hungarian Horntail knocks Harry off his broom in the first task, he can be heard screaming, but his lips don't move.
(at around 1h 18 mins) In the waltz scene, the orchestra includes a couple of boys playing saxophones which are not actually heard in the played score.
(at around 1h 50 mins) When the contenders enter the third task arena and during this scene, there are mismatches between the bass-drum sound and the video of the girl playing it seen in the background of the scene.
(around 56:30) As Harry is choosing his dragon, you can see Rita Skeeter's mouth move, but you can't hear what she is saying.
(at around 2h 10 mins) When Harry is in Moody's office after the third task, and Moody closes the cabinet door after searching for more potion, a crew member in a white shirt is reflected in the cabinet's glass.
(at around 1h 40 mins) When Harry is picking up the Licorice Snaps when the cabinet to the Pensieve is opening, you can see a glimpse of Harry's microphone box on his back under his hooded jacket.
(at around 2h 15 mins) When the camera moves to look into Moody's "pit-like" suitcase, you can see the shadow of the camera on the left.
(at around 1h 35 mins) The camera is reflected in the metal water container when Dumbledore walks down the stairs to attend to Ron and Fleur's sister during the second task.
(at around 1h 45 mins) The light of the camera is reflected in the glass behind Dumbledore as he talks to Harry immediately after the Pensieve flashback.
The Bulgarian national Quidditch team wears the colors of Albania instead of Bulgaria. Bulgaria's national colors are white, green and a much brighter shade of red than the Quidditch team robes. The maroon and black combination we see belongs to Albania.
Harry's first task performance doesn't attract any emergency actions from the Tournament's organizers, despite the fact that the dragon shouldn't even have broken its chains, not to mention fly away undisturbed, endangering countless people.
Barty Crouch Jr, disguised as 'MadEye' Moody, put the TriWizard's cup in the maze. Supposedly he put a charm on it to send the first person who touched it to the graveyard. In the book, there is no evidence that the TriWizard's cup was to be a port key for returning the winner to the start of the maze. In fact, in the book, it explains that Barty Crouch Jr turned it in to a port key and that it was not supposed to be one in the first place.
The possibility of putting someone else's name into the Goblet of Fire is an extremely careless act from the organizers of the Triwizard Tournament, as it carries a risk that an enemy could easily sabotage the safety of someone they dislike by putting their name into the Goblet even if the person himself/herself is not willing to participate in a life-threatening tournament.
The movie version left out the explanation how the Weasley family got their tickets for the Quidditch World Cup (and the character Ludo Bagman who gave them the tickets in the book), which raises the question in the movie version how the legendarily poor Weasley family could afford seven (ten in the book) of the highest priced tickets.
Sirius Black uses the Gryffindor common room's fireplace to contact Harry (presumably through the Floo Network, like in the book). This creates a plot hole, as if he has access to the Floo Network as a wanted criminal now, he could have used it in the last movie to enter the common room (as Floo powder can do that), but last year he tried to enter through the portrait hole (when he attacked the Fat Lady's painting with a knife).
(at around 42 mins) Harry's godfather Sirius Black is in hiding and using codenames in correspondence. Surprisingly, when he sends an owl post to Harry, he writes Sirius' real name on the envelope rather than a codename.
(at around 1h 35 mins) 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 Neville'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.
(at around 42 mins) When Harry receives Sirius' letter, at the bottom the letter reads "by the way, the bird bites". As Sirius' voice is reading out the letter, he says "P.S. the bird bites"
(at around 2h 15 mins) When discovered, Barty Crouch Jr. tells Dumbledore "Lord Voldemort is back". It is established in the Potter universe that Voldemort's name is not usually spoken (some exceptions being Dumbledore and Harry), let alone by Death Eaters, who do not dare to. Someone such as Barty Crouch would have said "the Dark Lord".
(at around 23 mins) When Alastor "Mad-Eye" Moody writes on the board, he incorrectly spells "unforgivable" as "unforgiveable". The letters surrounding the inserted letter are noticeably indistinct later on.