I noticed a couple instances in The Hour I First Believed by Wally Lamb where a who was needed instead of a that:
She said there were a few more people they still needed to reach, and a few THAT felt they had to decline, but that most of the eyewitnesses had agreed to assist them. (page 267)
"The woman THAT sat across from me in the bakery on our first date." (page 315)
That latter sentence was spoken by someone who may be forgiven for not always speaking perfect English, but the character was an English teacher, so I expected more of him. 😄
Not long after I got a new boss at my previous full-time gig, she questioned the use of whose when modifying a thing, not a person, in a sentence I don't recall in full. It was a legitimate question, and the legitimate answer is, our language doesn't have an accepted alternative for the possessive pronominal adjective whose when dealing strictly with things. See this post by Bonnie Mills (or Bonnie Trenga?) over at Grammar Girl's blog that uses the following two examples: "The car whose windshield wipers weren't working was driving in the fast lane." and "The tree whose leaves were falling seems to be dying."
For whatever reason, a word like thatse or maybe thats or even thatses, which would clearly show we're dealing with a thing, not a person, never took off as the logical possessive to use in such instances: The car thatse windshield wipers weren't working was driving in the fast lane. The motel thats sign was spray-painted didn't look like a place I wanted to stay. The novel thatses plot was getting too depressing for me is now back at the library, half-read.
That last example pertains to me and The Hour I First Believed. I couldn't bring myself to continue reading it once the author foreshadowed an even greater tragedy the narrator's wife was going to have to deal with after having already survived the taken-from-real-life massacre at Jefferson County, Colorado's Columbine High School, where she was a nurse. I didn't want to go where it was clear Lamb was going—to a chapter thatses next plot twist was too emotionally devastating.