Of course you can sue the seller. As the saying goes, "you can sue a ham sandwich."
I won't get into specifics, but an agent I met yesterday told me (several years ago) while she was showing a house, she fell down, broke both of her legs, and ultimately "sued the seller." Her financial settlement took 2 years and was more than 3 times what the home she was showing was worth. To this day she has back problems.
She didn't slip in the kitchen, but it does bring up the question: "Is the seller responsible for home safety while the property is being shown?"
My simple response is... YES!
The seller has invited the public into their house. In fact, they've all but SHOUTED: "PLEASE COME IN!" Realtors, buyers, inspectors, children, handicapped individuals, appraisers and even people who don't speak English will enter the property. If you have a huge hole in your backyard that someone trips in it, you could be liable. If they fall down the stairs because your carpet is torn, you could be found liable. The risks are real and they are there. It's important for home sellers to realize that the listing brokerage doesn't carry an umbrella policy for their listings. In reality, the outcome is your home owners insurance is simply... up for grabs. What if your dog bites someone?
We talk a lot about staging, marketing, pricing and proceeds, but not enough of us talk enough about safety! Last week I showed a home on a "private lake." Out back we found 3 snakes slithering around in the "high grass" in the backyard. What if my buyers child had gotten bit by a snake? Could the seller have been found negligent because her grass was almost waist high? Is it her fault the buyers let their child take off running through the yard?