Fizz's main problems are and always will be two things.
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The on hit damage he gains from his abilities. This is more in line with a bruiser or a tank, yet Riot wants you to play this champion as a squishy assassin. That doesn't add up.
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The "Troll Poll." No other champion has what amounts to indestructibility on a basic ability. Consider how broken it would be if Kayle could do short ultimate's on a lower CD as one of her basic abilities instead of as her ultimate, and it gave her a short dash on top of that.
However, for the mean time it doesn't appear like they will be altering his kit any time soon. They like the idea of Fizz as a slippery assassin. The problem he has is the same as Leblanc, when given too much power paired with that much safety they basically get to do whatever they want once they are fed enough. After a couple kills from roaming Fizz gets to decide when and where he will fight people and when he does he has a ton of damage and mobility.
I am not a fan of nerfing fizz though, I just want them to move parts of his kit around so that he doesn't do everything so well. If he is supposed to be a slippery assassin... great... make him an assassin. Not this bruiser hybrid thingy he always turns into.