I'm the kind of person who always feels like there's something I have to worry about, and I'll ultimately find something, no matter how silly it is. This was definitely the case when it came to my applications.
I think that for just about anyone applying to grad school, there will always be something that serves as fuel for anxiety. For me, explaining to myself over and over why I shouldn't worry doesn't really work. What does work is when I have the courage to say, "I'm not going to think about that," and just put my mind on something else. I might even say, "I'll think about that tomorrow," or next week, etc.
Learning to disregard anxiety is, at least for me, the best way to prevent anxiety.