Trivia: When Neville receives a Remembrall from his grandmother, it glows red to inform him that he forgot something. Neville says that he can't remember what he forgot. If you look closely, Neville is one of very few students not wearing his robe. He most likely forgot to put his robe on.
Trivia: When Hagrid is welcomed back to Hogwarts and everyone stands up and applauds, Vincent Crabbe also stands up and starts to applaud as well. This wasn't in the script and Tom Felton, staying in character, quickly grabbed Jamie and pulled him back down.
Trivia: In order to acquaint himself with his three lead actors, director Alfonso Cuaron had each of them write an essay about their characters, from a first-person point of view. Emma Watson, in true Hermione fashion, went a little overboard and wrote an 16-page essay, Daniel Radcliffe wrote a simple one page paper, and Rupert Grint never even turned his in, as he said that is what Ron would have done.
Trivia: Young Tom Riddle is played by newcomer Hero Fiennes-Tiffin, who is the nephew of Ralph Fiennes, the actor who plays Lord Voldemort, aka Tom Riddle.
Trivia: The costume department tried in vain to produce Luna's radish-like earrings. Evana Lynch made her own - they're the ones she wears in the film.
Trivia: There is an actual band in Canada called the Wyrd Sisters who tried to stop the November 18th release of 'Goblet of Fire' in Canada because there is a band of the same name in the movie, but they lost their case.
Trivia: Domhnall Gleeson, who plays Bill Weasley, is the son of actor Brendon Gleeson (Mad-Eye Moody).
Trivia: The banker who turns down Jacob's first request for a loan is named Mr. Bingley, an obvious homage to one of the main characters in Jane Austen's Pride and Prejudice. J. K. Rowling has stated numerous times in interviews that Austen is her favorite author, and this is not the first time she has alluded to her works with a character name; Argus Filch's cat, Mrs. Norris, from the Harry Potter books and movies shares her name with the busybody character from Mansfield Park.
Trivia: In the scene where Hagrid has dropped a "dead" Harry Potter, look quickly at George. He turns his head to the right and yells "Fred!" Fred has already been killed by Bellatrix Lestrange so it seems he may have forgotten this in a moment of grief.