Of course, none of my thats are, strictly speaking, wrong. They make grammatical sense. They are correct English. But they clutter up my prose like nick-nacks on a Victorian mantelpiece. The speech rhythms are clunkier. Take the Anthony Trollope title He Knew He Was Right. How much more stylish that He Knew That He Was Right. One version works, the other doesn't and all that divides them is an innocent little that.
Most documents I write I have to run a speedy search and destroy mission for superfluous thats using the Global Edit facility. It takes ages, but I'm happier as a result, and my prose reads just that little bit more easily. (That one passed the that test.) One of my writing friends is fine on thats. Her problem is adverbs. Another has a fondness for exclamation marks. We all have our writing problems. I know I am a Happy Thatter. What's yours?