I learned this day one in Building maintenance: if you just put a tennis ball on the end of a mop stick, you can remove most floor scuffs. Just rub the scuff with the tennis ball. This is a great janitorial tip.
We discovered a while ago that if you are having a problem with cleaning floor grout, any product with a percentage of hydrogen peroxide will do the trick. After a few cleanings, you will notice the grout releasing the stain.