Ain't No Rule: Part of a Batman Gambit by the current King. He deliberately set up the rules so they did not specifically ban Celestial or Infernal children being chosen to fight, knowing that this would cause some of the King Candidates to think they were getting away with something by inserting "ringer" champions. It didn't turn out quite as well as the King hoped.
Art Evolution: While the art style of the manga may appear a bit strange throughout, there is a very noticeable improvement from the style in the first chapter to that of the later chapters.
Autodoc: Heavenly Beasts release a healing machine which fully restores anyone inside it for exactly 10 minutes. However, if the healing process is interrupted in any way and the machine is damaged, the person inside it will die.
Inumaru also lampshades it at one point, surprised that someone so conniving but loves justice so much went into teaching junior high school.
Bag of Spilling - Between Law of Ueki and the short five volume manga sequel Law of Ueki Plus. Justified, as if Ueki uses any of his old special abilities it would result in the loss of his Zai and he would die, because the tournament is over and therefore nobody is a combatant now.
The strange part is that 9 from his 12 powers were weapons, and one is a Cancelator, but he has also some Jet Skates, and a pair of wings. Also, he could try to use his powers in a way that wouldn't harm anybody.
Badass Normal: Mori, since her power is pretty much useless and has only been used twice in the whole story. It's justified that her limitations is ridiculous (goody-two-shoe pose, anyone?). But when she fought in Dogura Mansion, it has been shown that she had fought to a tie with Kabara, who's an assassin to boot.
Chew Toy - Ueki gets into a lot of situations that end up with him getting hurt in some way. Mori Ai even notes that this happened to Ueki even before the tournament started. Although most of those were the fault of Ueki's brashness, a lot of random events also seemed to be detrimental to him. It is later explained that this was due to the loss of a good luck zai of some sort.
Cross-Dressing Voices: Romi Paku played the voice of the main character, Ueki Kousuke, who is a guy - and shows not one bit of girliness in him.
Determinator - Ueki. In fact one of his opponents is defeated by his determination.
Discard and Draw - Ueki loses all his abilities at the end of the manga. In the sequel he gains a new power: The power of "grabbing" in the form of "a mop".
Disproportionate Retribution - the punishment for a god candidate helping their junior high school student in a battle is to be put on celestial death row. Even if they only do it to save a kid's life.
Fetish - Mori's power gives her opponent a HUGE eyeglasses fetish. ...And then there's Kill Norton, who glued his glasses to his head. Granted, it was in case he got paired up with Mori so he could have a way to counter her power, but still... Also, his glasses are named Bianca. Later, he asks Mori to make him an eyeglasses lover again, so he can work up the nerve to go help his teammates fight Anon. The last time we see him, in the epilogue, he's muttering "Glasses... glasses... glasses..."
For the Evulz - Anon helps humans then proceeds to harm them immediately afterward just to find out what kind of reaction he will get (like rescuing a boy's puppy and trying to throw that puppy to an electric pole).
Funny Afro - Ueki temporarily gains one along with a Disco Zai ("talent to dress stylishly" in English). Apparently, Ueki was following the good ol' Saturday Night Fever style. He was immediately beaten up by Mori.
And one celestial beast wears one near the end, and immediately gets a lampshade hanged on it.
Idiot Hero - while Ueki does have several brilliant insights, especially in battle, for the most part he seems rather simple-minded and clueless. On first meeting Tenko's gigantic dog-like form he thinks it's just a really big chicken of all things.
This is actually explained early on in the series, when Ueki loses his Study Zai ("talent to study") for attacking a non-combatant before the tournament begins.
Kirk Summation - The purpose of the tournament was so the King could try to get the Protectorates to see that times had changed and they had to stop living in the past and start looking to the future. He even gives a speech about it to the Protectorate controlling Margaret. It doesn't go as planned.
Last Minute Hookup - Ueki and Mori officially become a couple at the end of The Law of Ueki Plus.
Meganekko - Rinko, Mori has glasses too ( and her powers are based around them) but she doesn't ever wear them over her eyes.
well almost never since the Q&A in the final volume sates that she is long sighted and so they are reading glasses
It's implied Mori's glasses are purely to invoke this trope, as she carries over a hundred pairs with her, even before she found out about her power.
Magic A Is Magic A: The setting is not consistent with those rules, though. It's explicitly said that every power has its limiting conditions. And yet not only some of the power users don't have any conditions - Sano, whose condition (holding his breath) is explicitly stated, freely talks while using his power.
Off Model - Happens relatively often in the manga. Some panels just look weird...
Official Couple - Ueki and Mori. While not explicit in the anime (although there are are a few subtle Ship Tease moments) it is made clearer in the manga and becomes fully canon by the end of the sequel series, The Law of Ueki Plus.
Screw This, I'm Outta Here: Hideyoshi does this to Team Ueki at the end. However, he couldn't abandon his friends in the end, and by coming back at the last minute, He saves Kosuke's life by getting knocked out by his Kurogane attack.
Sink-or-Swim Mentor - while Koba-sen, Ueki's God Candidate, has a strong sense of justice, he is laid back to the point that he pretty much leaves Ueki to figure out his powers by himself. To be fair, though, those are the rules. When he does step in to save Ueki from certain death—against the tournament's rules—he promptly suffers from the Mentor Occupational Hazard. Though he doesn't die, he is sent to Hell.
However, Kobayashi never told Ueki about the tournament, its rules, or the prize until after he'd already gotten into a fight. Everybody else knew all the specifics well before then.
Enemy: Do you want to know what my ability is? I'll show you. When I squeeze a stone, I can...” *tree hitting a face, knockdown*
Teens Are Monsters - All of the contestants in the tournament are supposedly junior high school students, yet a lot of them want to be the champion in order to take over the world, and have no qualms about killing their opponents.
Too Dumb to Fool - BJ starts off trying to win fights by claiming to be Robert Haydn, which causes people to run in fear. While Mori falls for this, Ueki just remembers that BJ introduced himself as BJ earlier that day, and just can't seem to understand BJ's claims that his name is really Robert Haydn... And keeps insisting that he's really BJ. The fact that he doesn't even know who Robert Haydn is probably helps.