I think one of the more controversial aspects about Hearthstone is balance and how it's accomplished and the speed of it.
While not talked about much, I think the decision to always keep the base set in standard is odd. It's very arbitrary. There's nothing really special about it in the sense of they did not design a polished set to be permanently in standard. While some cards certainly make sense to be permanently in it such as fireball or eviscerate as they are very basic but effective, when you get to many other cards it's hard to explain why they are permanent but others are moving out.
I think if you asked them, there would not be any attempt of a logical explanation of why x card is staying but y card is rotating out. You could do this with just about any legendary basically from the base set. And multiple other cards.
I would like to see it get at least 1 attempt of making it refined. I think adding some cards to the base set (Reno suggested a lot) is another possibility. Regardless, would like to see more effort put into it.
As for the speed of balance, outside of cases of extreme imbalance, they almost never actually nerf cards. And when they do, it takes months for that to happen. Is this the right way to go? Instead of saying "oh, it'll rotate out eventually", should they actually be proactive and nerf the card in a reasonable amount of time?
Coming from WoW (as I think most here play currently or in the past) I would like to see things get proactively nerfed more quickly when they see an overpowered card as WoW does. (Even WoW is slow but it's light speed compared to Hearthstone)
On paper id like to see some cards buffed but I think that's too risky.