What do you consider "Broken"?
it should be a surprise to No one league of legends is a massive game. In a game this big there will be oversights. Lets talk about them. keep in mind this is Opinionated and well my opinion is less then popular at the best of times.
Mid: Prechamp select make sure you have the thunderlords talent Why? because thunderlords procs with tourmented soil ticks. All you have to do after that is max tormented soul, you instantly farm waves and occasionally get a Thunder lords proc on an enemy champion.
Kind of the same deal with morgana only its worse. thunderlord and max malefic visions. Malzahar is worse IMO because, he has a point click suppress there aren't many items that counterbalance suppress. with malefic visions you have no hope of getting a minion advantage it bounces from minion to minion. and has a change to bounce back to you. if done right you just eat about 500 damage of malefic visions and 100 I just feel like its exploitive and goes to far it makes champions like Akali, katarina, and Zed (Some of the very few AD mid champions) completely worthless.
I know teemo has a lot of hate and its for a good reason. you gave a rat I could punt 60 yards on a foot ball field the ability to blind you for 3 seconds while scaling super well in AP or AD. I am surprised No one has tried Hybrid yet. so what is the problem here? basically he makes every one want to just not play any more. His laugh is annoying his fanbase are a bunch of jack asses. not to mention the best way to play him is siegemo. (CDR Ability power and magic pen) just one of his ability power shrooms cuts your health pool in half reguardless of how much magic resist you build.
What more could an ADC want? Point click blind, a broken move speed buff. A passive that prioritizes champions. It is a real shame Not very many people play her because, she is nearly freelo. she is one of the few champions that position doesn't matter with.
any one of these champions are problematic to play against. Most of them are problematic with thunderlords in toe but, reguardless one ability free farming a wave forcing their enemy to farm under a tower is all to unfair IMO.
and the torment began ='(
its really bs that his only counter is group. too much damage, cant be kited, heals too much, and has no drawbacks for being shit on early, needs more counterplay other than saving cc and grouping
all these champs, i usually play utility mages or junglers, and these guys piss me off, if i go vel koz, i can e q, whatever, these guys all i want, and they still come at me and 1v1 me with only 1 damage item, and i maybe do 1/5 of their health with my full combo. like its so bullshit that a black cleaver garen can take no damage, but kill you faster than a zed. same with voli, and all these other champs, too fast, and too tanky, and not much room to kite them with, especially with all their movement speed increasing items 
can out do him in what he does 1 on 1. Otherwise he can be shut down by one stun, root, or anything of the kind. He's designed to be a hypercarry and has tons of counterplay like Kat.