deep-cleaning vinyl flooring

[slyph]

I just moved into a new flat with vinyl flooring that looks like it hasn't been properly cleaned in years. When you look at it up close there are places where there seems to be a thin layer of grit embedded in the vinyl which I can scrape off with a screwdriver. Also, there seem to be a bunch of little paint spots all over the floor, which blend in from head height but are pretty noticable up close.

What is the best way to fully clean the floors? Is it safe to scrape them lightly with something? Will that "floor stripper" stuff they sell work to get up both the grit and the paint?

Thanks!