In alphabetical order since I am bored:
Ahri's Charm shouldn't affect female champions.
Caitlyn's Peacemaker & Ace in the Hole should shoot at regular timing, like her auto attacks.
Considering Cho'Gath eats things with his basic attacks, he should grow bigger regardless.
Corki should be able to fly over walls.
Draven's ultimate should go on indefinitely. If he can't control exactly where his axes should land when rebounding, he shouldn't be able to magically command them to come back to him (and reset their damage...).
Elise's Cocoon should be a snare not a stun. That slow moving ribbon thing is not going to surprise or stun anybody.
Fiora's Blade Waltz shouldn't make her untargatable, jumping or not. Things like AoE damage especially should still affect her.
Fizz's Trickster shouldn't dodge spells that were already coming at him. That makes no sense at all (especially since Maokai's Twisted Advance doesn't).
Galio's Bulwark should hurt him instead of his target, not heal him.
Gangplank's Cannon Barrage should have a charging time. His ship cannot randomly prepare and fire cannons all of the sudden, also, they should come from a slight angle, not straight down like they do. Remove Scurvy shouldn't get rid of all crowd control effects, oranges are not a cure-all (lol).
Garen's Perseverance....Having perseverance does not make you heal over time. What are you thinking? Same goes for Courage, which does not physically make you any more durable.
Gragas. Throwing barrels does not heal you, nor should Drunken Rage give you mana...and the damage reduction should just be that he perceives to feel less damage, not is actually dealt less damage.
Grave's Quickdraw should not increase attack speed at all...why does it do that? Also, his ultimate is mislabeled, as Collateral Damage implies that the damage done would include a member or item on your side/team.
Irelia's Hiten Style should make her basic attacks do true damage at all time, not only when active.
Janna's Tailwind should only be active for nearby allies, who are behind her (like the enchantment). Eye of the Storm is a defensive gale, which means that it shouldn't give attack damage.
Jax's Counter Strike uses his "combat prowess" to dodge attacks. This should be active at all times. If you have it, you don't need to activate that part of your brain in order for it to start working. The same goes for Leap Strike. Jumping? You can do it as much as you want.
Karma's Heavenly Wave shoots blades. Blades. These should not heal allies (forget the fact that allies aren't harmed).
Katarina's Voracity shouldn't reduce her cooldowns. It could increase her damage by empowering her or something, but reducing cooldowns? What is that... and Shunpo has no reason to give her damage reduction.
Kayle's Holy Fervor is a misnomer. Holy Fervor, since it's called that, should increase her attack speed or something, not reduce armor/magic resistance.
Kennen's Slicing Maelstrom doesn't slice at all, it's electricity. And its image has shurikens in it... just no.
Alright. I'm done. Not naming anymore unless I feel like it... There are a lot of champions...