Would be a good idea for a game but would be easy to screw it up. a la "turn based" action and lame azz quests.
If they made large cities or even just one (so large it would take days to walk across like in real life), with buildings you can explore, that would be step one. Another would be live action combat (not turn based crap) with first person/third person capability. And no level based crap because level based areas and zombies would be real real lame, have skills that raise like discussed below (similar system to Oblivion and Darkfall Online for those who played that). Also, there would have to be something else to the game besides who can hide in the tree the longest, but also have rewards for people who meet those types of achievements (live the longest, kill most zombies, etc) and I'm not talking about lame azz quests like most MMOs have. That something else could be actually saving other players who are surrounded by hordes of zombies or raiding a grocery store for supplies because your character is (literally) starving to death, or raiding a gun shop for the few bits they have left because all you have left is a baseball bat. Maybe even allow players to gather stuff to setup some sort of half-way safe "base" (that can be and most likely will be overrun).
Items to find/make could be numerous guns from fallen players or gun shops you come across, melee weapons, flash lights, food/water, first aid stuff, clothes with different slight benefits (dark for hiding in shadows, diff shoes for quieter walking, etc).
Skills could be plentiful allowing various character setups and could compliment the items in the game. Skills could include endurance for running longer, sneaking, scavenging for food/water, better first aid, weapons would be FPS style action so skills probably not used to enhance that (think twitch FPS, based on player skill).
Also, doesn't always have to be dark (that would be lame), daylight is okay some of the time.
Those are just a few of the ideas that I think would make a good zombie MMO.
A big question is how big of an MMO do you make it? If you put too many humans in there, then you could have them turn into zombies (zombie skills would be lame I think, special attacks other than lunge or maybe slight run would be retarded, they're supposed to be somewhat weak, power comes from numbers). If the player didn't want to play zombie after they turned, they could reroll their char but that zombie is still in game and controlled by CPU until it dies (could be abused by purposely spawn deathing a ton of zombies so that would have to be looked at by the producer). And does the server restart when all humans get killed and only zombies left or are new humans allowed to join in? How do new humans join, are they "travelers from other areas in seek of refuge"??
That's my dream zombie MMO.