Well, we finally have a concrete sense of how we're going to function in a world without hit, expertise, dodge or parry on our gear, thanks to the Warlords of Draenor alpha notes. So far, it looks rather interestingly painless.
First up, dodge and parry as stats on gear are gone and the amount of dodge and parry we get for agility and strength, respectively, will be reduced by 25%. Active mitigation is in, avoidance is out. You can still get some small amounts of dodge or parry from class-specific effects (Riposte, for instance, has been reworked to give 100% parry after a critical strike until you parry an attack, and it can stack up to 2 times, meaning you can have two parries in a row before you lose the 100% parry from Riposte) but in general, you won't be able or willing to gear for those stats anymore.
As for hit and expertise, their removal leads to the change in design to balance out how we hit things. Against monsters and such up to three levels higher (including bosses, who as skull level are always three levels higher) you'll have 100% chance to hit, 3% chance to be parried, and 0% chance to be dodged. This means that you'll still want to be standing behind them if at all possible. Tank classes, however, will have an extra 3% parry reduction baked into their tanking specializations, meaning that they will have 100% chance to hit and 0% chance to be parried or dodged. They can stand up front.
Dual-wield classes (rogues, enhancement shamans, frost DK's, fury warriors, potentially windwalker monks) will have an additional 17% chance to miss with no way to improve it in order to balance their DPS out against 2h users.
For the complete list of the removed/changed abilities that once granted hit or expertise or which now reduce chance to be parried, the full list is behind the jump.