I don't worry so much about the liability part of it as I have insurance that would cover me but I do worry that the parents would think I wasn't doing my job and blame me. (not that it's our fault!! kids have accidents) I (knock on wood) have never had a major accident in my home yet but I'm sure it will come one day!
My other half on the other hand worries that a parent would sue us if something happened. He is pretty anal about things so he always fixes broken things asap, makes sure the walkway is always cleared, ice melt is out etc.