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: 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: In the scene where Harry and Malfoy are flying on their brooms, there's a shot where Colin takes a picture. Listen to the music right after that. The music is the same music used in Star Wars: Episode II - Attack of the Clones during the chase scene on Coruscant (John Williams did the music for this film and all the Star Wars films).
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: 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.