The violence against zombies becomes so cartoonish that it doesn't bother me, though the filmmakers do go out of their way to make it gross.
The violence against humans usually doesn't bother me either. But then, I have a fairly strong tolerance for violence unless it's super gory or is the whole point of a plot (like, I would never see a movie like "Saw" or even supposedly higher quality ones like "Se7en").
There have been a couple of pretty shocking human killings on TWD, though. And I think the worst thing I've ever seen was this past half-season and it didn't even involve killing (Chuck, you may know what I'm referring to). Actually, this whole past half-season has been pretty gory.
One thing I realized years ago, when watching the movie 28 Days Later, (also a zombie movie and is actually quite good -- I would recommend it!) is that the source of tension and fear in zombie movies isn't the zombies. Unless they swarm you en masse or you have your leg stuck in a trap and can't run away or whatever, zombies aren't much of a threat -- they're slow and stupid and in this case, easy to kill. The tension and fear comes from the relationships between the survivors. That was true of 28 Days, and it's also true of TWD.