The more I play against hunters the more I think the class has a big balance problem, the sheer number of them out in Constructed says it all really.
Off the top of my head.
1) Their hero power which is flat 2 damage directly against your hero every turn from turn 2 onwards (or even turn 1 if they coin it). OK a priest can heal for 2 every turn, a druid can lob 1 armour onto themselves, a warrior 2 armour and what have you, but these are all reactive and defensive. The hunter gets a straight 2 damage every single turn which puts you against a hard turn cap without anything else at all going on.
2) UTH and even more so the Leeroy > UTH combo means you can never have more than a couple of minions on the board, the risks involved with going above this are too great. This means you need to play slowly and conservatively. Generally speaking a 'blitz' turn needs a turn to set up, you set that turn up and you get UTH-ed - game over. (Add Leeroy into the mix and it starts to get ridiculous IMO.)
3) Too many cheap cards that buff UTH. Starving buzzard and timber wolf specifically. You have to assume that every hunter is running with two buzzards, wolves, and UTHs, and play around the chance of there being a Leeroy in there. This limits your play massively, and every turn you've got the tick-tock of the hero power.
4) A decent selection of hard removal cards, such as deadly shot. On paper 'destroy a random minion' doesn't look as good as say a poly or a hex, but when you can only ever have two minions out on the board, it becomes a very powerful card. Multi-shot is also a good early game spoiler for them, and explosive shot is powerful too.
5) They can slow you down with secrets. These are fairly predictable and can be played around, but they slow the game and you've still got the tick-tock of the hero power.
6) Insane card draw ability, even a 'non-lethal' UTH can draw them a large number of cards, fuck up your board, and you know they've probably got another one to play as soon as they fancy. And let's not forget tracking either... I can't think of any other class that can achieve the cards they want to be in their hand as quickly and easily as a hunter.
7) A decent selection of other quality cards that give them good options for most situations. Arcane shot is cheap and effective, hunter's mark is pseudo-poly/hex effective and costs zero mana! Kill command works well, houndmaster can slow you down in a game that you're already playing slowly, and so on.
I'm sure they're due a nerf sooner rather than later, what I think is really telling is that in a game where a hunter doesn't play UTH, I pretty much always beat them. Having a whole class revolve around one card combo isn't right.
By all means give them other stuff to compensate, but make the class interesting to play, and interesting to play against.
I got the hunter class legendary in my 40-pack card splurge the other week, and I haven't even bothered to try and play with it, because I know I still need the cheapass UTH shit in the deck, and I refuse to play like that.