Donnie Smith's parents used the money he earned during his time in What Do Kids Know?
Jimmy Gator quite likely molested his daughter Claudia, though it's hard to say with certainty. She's a drug addict, which could be her response to such an event, or warped her memory into believing it. When confronted, however, his only reply is an apparently sincere claim that he doesn't remember, which is frightening on its own. Also noted is his invasion of her bedroom earlier in the movie. This gives the sense that he is dismissive of personal space and thinks himself entitled to his daughter's time at the drop of a hat even though he knows of his status as a possibly-still-dangerous abuser in her mind.
Rick Spector constantly forces, manipulates and guilt-trips his son to win. Like Donnie's parents, Rick profits from his son's efforts.
The parents of the other two quiz kids.
As the Good Book Says: The arc numbers 8 and 2 appear throughout the film. They refer to Exodus 8:2, in which God calls the plague of frogs against Egypt. The film climaxes with just such a plague falling over Los Angeles.
Also, contains a subversion with the line "And the book says, we may be through with the past, but the past ain't through with us," spoken by multiple characters. The book in question is not the Bible, but The Natural History of Nonsense a 1946 anti-superstition book by English professor and game-show host Dr. Bergen Evans. When first we see Stanley in the library simultaneously contemplating multiple books, The Natural History of Nonsense is among them; it is in the center-right, and has a blue cover. (Perhaps on the big screen—or in HD—the book's appearance is not as difficult to discern.)
Apparently the powers that be weren't aware of the Biblical connections to the rain of frogs. Once they were informed, they decided to sneak in the 8 and 2 references all over the place.
Billing Displacement: Where's Alfred Molina? Oh, there he is. In one scene early on in the film. Despite of this, he is even credited above Melora Walters.
Cluster F-Bomb: Most of the film's characters could fall under this trope (Good examples are Marcy and Claudia's beginning scenes). However, none of them can seem to reach the extent that Linda Partridge does with this trope. She says the word "fuck" in virtually every scene she's in, and it's usually never uttered just once.
Linda Partridge (to the pharmacist #1): You motherfucker. You motherfucker, you fucking asshole, who the fuck are- who the fuck do you think you are? I come in here, you don't know me, you don't know who I am, what my life is, and you have the balls, the indecency to ask me a question about my life? (to pharmacist #2) And fuck you too, don't you call me lady!... I have sickness all around me, and you fucking ask me my life? What's wrong? Have you seen death in your bed? In your house? Where's your fucking decency? And that I'm asked fucking questions, what's WRONG? Suck my dick! That's what's wrong! And you! You fucking call me lady!
Country Matters: We're introduced to Tom Cruise's character as he's leading a chant: "Respect the cock! Tame the cunt!"
He-Man Woman Hater: Frank T.J. Mackey. "Respect… the cock! Tame… the cunt!" Eventually revealed to be something of a subversion. Mackey's real hatred is for his father (and himself, in that he loves and leaves them just as his father did), and part of the reason he treats women poorly is because he can't stand the thought of getting close enough to one that he'd love them the way he loved his mother.
Hyperlink Story: All the characters link together in one way or another. The end credits to "What Do Kids Know" reveal that Earl Partridge is the producer of the show.
Promotion to Parent: Stanley, hurrying to get ready for school, reminds his father they're out of dog food: promptly—and almost imperceptibly—establishing which member of the Spector household is fully-engaged and responsible. In the green room—after the on-air meltdown of the show's host, and its brightest contestant—Daddy throws a tantrum (and a chair). Role reversal complete: as a parent, Rick has been invisible.
Recycled Soundtrack: Aimee Mann's "Wise Up" was originally written for Jerry Maguire, and several of the other songs were meant for her album Bachelor No. 2, which was recorded before the movie but due to record-company problems not released until afterwards.
Phil: I know this sounds silly, and I know that I might sound ridiculous...like this is the scene of the movie...where the guy is trying to get a hold of the long-lost son, y'know, but this is that scene. This is that scene. And I think they have those scenes in movies because they're true. Y'know, because they really happen. And you gotta believe me, this is really happening. I mean, I can give you my number and you can go check with whoever you gotta check with and call me back. But do not leave me hanging on this. Please. I'm just — please. See...this is the scene of the movie where you help me out.
Truth in Television: Believe it or not, frogs and other creatures raining from the sky has actually happened on more than one occasion. When a particularly heavy storm or tornado sweeps over swampland filled with frogs, it isn't that unusual for the animals to be swept up in to the air and dropped on nearby land.
Urban Legends: No, the three anecdotes that open the movie are not true stories. The last anecdote, about the man shot while jumping off the roof of a building, was also used in Homicide: Life on the Street, and is also apparently used as a test case in criminal law classes.
Waxing Lyrical: Several lines are quoted or paraphrased lyrics from Aimee Mann songs, the most obvious being the opening line of "Deathly":
Claudia Gator: Now that I've met you, would you object to never seeing me again?