I've never heard of Vim before. I know Vinegar is great for everything, my mother swears by it. LOL
TSP is worth a shot.

Tilex I've used before, but required much scrubbing. But maybe I could find a different type. I have used CLR before too when I lived in a place that got really bad rust stains in the tub. It worked great, so that might be a plan too.

Well thank you all for the great ideas! I'll see what I can find and I'll let you know which works best for me.