A zombie was once a human, and so it has the properties of the human body: hard bones, thick flesh, joint cartilage, etc. So, the bodily toughness of the players and their undead assailants ought to be about the same. The primary question to be answered is what it takes to stop a zombie from being dangerous.
I ask these questions of myself: How much damage can a zombie really do to a person? At what point should a zombie stop being a threat? Should blowing a zombie's head off make the zombie stop attacking?

A zombie bites through the back of a victim's neck in order to sever their spinal cord.
I think zombies should be strong. They should not be able to move quite as fast or as agilely as the living, but they should move in a motivated fashion and desperately grab onto their victims once they are within distance. Once latched on, they should throw punches, bite, scratch, gouge eyes, and otherwise employ the worst of deadly fighting tactics to bring their opponent down. When zombies have beaten and surrounded a victim, they bash the living victim's head wide open so that they can gorge on brains and blood.
This is in contrast to the view of zombies that I have seen in some movies: slow-moving, unmotivated, launching ineffective attacks at opponents.
The next area I'm interested in deals with zombie destruction. It is a well-known fact that a shotgun is a good way to deal with zombies. However, some others seem questionable.
If you have a pistol, what is it going to do to a zombie? Against living foes, it's great - putting a hole in somebody is sure to mess up the bloodstream, and possibly cause an affected organ to fail. However, what if anything should it do to a zombie? Zombies don't need blood or a beating heart or a working brain, do they?
It seems to me that the ideal way to stop a zombie is to make him less dangerous, and less mobile. This starts Holy Grail-style by chopping off arms and legs. Removal or heavy damage to the zombie's head should disorient the zombie, either causing it to stall in action or causing it to charge and flail wildly in random directions.
A shotgun can blow off an arm or leg or head. This makes it a good zombie-killing tool. A big knife can remove limbs as well. I hate to ask, but does anybody have any idea how hard it is to remove a limb from a body? Can it be done in a hurry? A sword would be better yet. I personally believe that the ultimate zombie-killing weapon would be a katana, allowing its wielder to quickly remove limbs from attacking zombies. An automatic rifle might also be quite effective, allowing you to essentially rip a zombie in two.
So, where does that leave household items? Each house generally has a few big knives. A baseball bat could break bones or smash heads, doing a fair job at disabling zombies. Chairs and table legs can act as similar bludgeoning weapons. Many households have chainsaws, which while not being very easy to wield, can presumably dismember a zombie pretty well.
Reader, tell me what you would use to kill zombies if you were put in the situation. Tell me what you think it ought to take in terms of physical strength, time, and skill. Could you personally take on two zombies at once? How about five? Could your sister take on a zombie? How about your mom, or your grandpa? Do you think that each zombie after the first would get progressively easier to kill, given the practical experience that you would gain?
For martial artists in the audience: do you think that you could actually dismember a person if it came right down to it? Could you break so many bones that an assailant wouldn't be able to grasp you? Can you effectively break the legs of others using kicks that do not harm your own legs?
These things I want to know. Help me out here -- I want to make the most mechanically realistic damn zombie game BYOND (and the world!) has ever seen.
Creative Commons credit for zombie pic: j.lee43's Flickr photostream - picture here
I think the best way to kill a zombie is with a cricket bat.
Also, can people become zombies in your game? In that picture, the zombie is trying to break the spinal column That would paralize a person, and I would think it would do the same to a zombie also. I tend to believe that if zombies were once human then they still operate basically the same way humans do. Meaning that the brain is still a vital part of their body. Also, can zombies be poisoned? How about feed them some bleach or something.
I don't know just random ideas.