Most of the items in the game are balanced, it's the champions that abuse them that is the problem.
The only truly broken items in the game are
and arguably

The problem with Rylais is that the premium stats mean that a lot of carries would get the item solely because of the stat bonuses. The slows are a whole other story.
Rylais is so abusable because of the DOT portion and the AOE portion. The AOE portion has the duration halved, but that doesn't mean anything. Most AOE's have lingering effects
for example means the duration cut is absolutely nothing. They don't feel it at all. They still get the slow for the full duration of the AOE at the same potency. Coupled with the fact that you can follow it up with potentially 3 other abilities that also slow, this is too much.
Fix: Keep the numbers as is for stat boosts. Bring the AOE slow down to 20% and the duration back to 2 seconds. Theres now a debuff on each champion effected by the rylais slow saying they cannot be effected by rylais slow for another 7 or 8 seconds or so. This keeps the slow and adds a cc, but doesn't give you a free permaslow for buying the item.
Black Cleaver lies in the passive. Reducing enemy armor by 30% means that youre gonna hurt from this item alone. It's why juggs can buy this item and wreck face, because the stats from the item insure that they will be pumping out loads of damage.
Pre buff this thing had nowhere near this much overloaded stats. It has everything a bruiser wants. Sticking power, Health, AD, half the max cdr on one item, and armor shred.
Fix: Either vastly lower the armor shred, or remove the rage proc altogether, and put the cdr down to 10%.
Dominik's....I'm speechless.
If you're a tank, and they buy this item, you might as well sell your tank items and go damage. Buying this item just means they cut through you like butter. We have tons of % damage increase in the game through masteries and items (There's even a 10% boost ON THE ITEM.) , we don't need to ignore half the damage resistances too. That needs treated. I don't know an appropriate fix without completely gutting this item.
And Duskblade, is gonna get changed preseason.
Items like Frozen Mallet and Trinity force aren't broken in themselves, it's because of the champions who abuse it. Try building Trinity force on anyone that doesn't instantly apply the on hit effect and back off effectively. This is because stupid champions like
exist and the item basically just gives their poke a 200% bonus ad ratio. Imagine that. This really good stat item, just gives your primary poke option a 200% bonus ad ratio. That would never make it past testing.
It's because the item itself isn't broken, other champs haave to commit somewhat to get that item damage off. Nope, its just the select few who abuse it this way.
Frozen mallet isn't broken because for the most part it's lackluster in stats and the only reason you build it is to abuse the slow. The only champion I can think of who can't totally abuse it to it's limit who would build it and not have a wasted slot would be
. No this item is busted because champs like
are completely and totally unkiteable, with countless mobility, dashes, and already existing slows and hard cc, yet they are primary auto attack based, so these champions assure that you 100% will not get away without flashing.
It's not the items. The only broken items are the four mentioned. If something is broken, it's because someone's abusing it. You don't throw the gun in jail for killing someone, you throw the person using it.
This is literally abuse. I've got Thresh's Attack Speed so high, that his attacking animation glitches.