Before the advent of antibiotic creams and pills, simple scrapes and cuts were a treacherous endeavor even for healthy-as-a-horse humans. Cuts allowed dirt and germs to get a little wiggle room and make their way into your innards. But with proper hygiene, including wound rinsing and hand washing, most people eventually recovered from these kinds of injuries, although the healing process took longer and sometimes resulted in long-term side effects.
Whereas humans have tissues that can regenerate and heal themselves, zombies do not. Their wounds, no matter how mild or severe, are permanent. Imagine, if you will, a paper cut that not only doesn't heal, but actually becomes wider and deeper by the day. As the flesh continues to divide, the bone is revealed, and eventually the last drooping flaps of flesh fall to the ground.
A small scrape would blister into peels of skin that sag and slide right off of a zombie's body. Skin charred by burns would curdle into a goopy, grimy mess. And all of this decomposition would be for the best — no one wants to be a zombie for long, anyway.