I have heard pro sculptors discuss using acetone as a smoothing agent on the surface of clay. After the sculpture is finished, but before baking, use a soft bristle brush and stroke the surface with the acetone to remove final fingermarks and tool lines.
I have not done this myself, though...
As far as the marks you're seeing "in" the clay - I think what you are describing are often called "moonies" or "plaque" by most clayers. They're tiny bubbles under the surface of the clay, which once baked appear to be tiny white or beige circles, right?
Nobody is quite sure what causes them. It might be moisture, or air. They are most visible in translucent clay, because the light passes into the clay and reveals them; opaque surfaces hide them. EVERYone gets them; some techniques like faux stone even use them to advantage. But when you don't want them, they're very annoying. Unfortunately, I don't think anyone knows how to prevent them completely.
Some things that will minimize them, though; be sure when you are conditioning your clay that you are not introducing excess air or moisture to the clay - handle it carefully - if you use a pasta machine, always put the clay in with the folded edge closest to the rollers, or at least sideways. Don't mix any wet ingredients into the clay (such as alcohol inks for color). And make sure you're not working in a warm and humid room where sweat and condensation might be added to the clay.