Variable damage is in the next playtest draft. I'm less sure of class specific hit dice after some testing, but it will probably be in the next playtest draft as well. It may or may not remain depending on what playtesters think.
I'm inclined to agree on both accounts.
Regarding class-specific hit dice, it would seem that lowering a magic-user's HD to d4 would severely impact their ability to cast spells in the long run. Conversely, upping the fighting types to d8 or d10s might make them much more powerful thanks to added endurance, especially when using the advanced combat maneuvers.
I think my only reason for wanting class-specific hit dice in the first place is tradition. Fighting types are tougher than magic-users, etc.