Mulligan for fiery war axe (aggressively) and/or whirlwind / acolyte / frothing - especially against aggro decks (hunter, zoo, the faster mage version, shaman, etc).

One of the decks that can beat this is handlock. The matchup is difficult and very draw dependent for both sides. Execute and sylvannas+brawl are your friends. Same goes for the matchup against control druid (don't be afraid to double-axe the turn 1/2 yeti though).

There's also a warlock version running arcane golems + power overwhelming + faceless manipulator. Only taunts can save you from them, but even then it's really hard to win (combo beats control).

Always clear boards and try to maximize draws from acolyte.

The deck used to run harrison jones but i never had any real use for him except maybe against a paladin. Consider exchanging MCT or senjin for a silencing minion if facing too many Tyrion paladins, but that will probably make you face only aggro after the change, in which case MCT can be exchanged for a second senjin. 

Alexstrasza is not in the deck because i never found a use for her. You either stabilize before turn 9 anyway, or you die from some combo or a too fast deck. If the presence of aggro decks is reduced, consider exchanging Geddon with Yasera or Deathwing. 

The deck's weakness is, as it always has been, draw power and reactiveness. Not stabilizing during the mid-game (or at least exchanging heavy blows) usually means defeat.