Well, pretty much all solutions have been covered. If you can avoid 80 grit, do so, because some times the 80 grit scratches are worse than the tool marks you are trying to sand out.
I use the same progression that Mark does. Mostly when you do leave some scratches from two grits ago, if you are going in half steps, you can get those scratches out, without having to go back another grit.
Having good lighting and glasses really helps. We all see differently, but I like the natural light spectrums. The main reason for that came from a quote from a turner on another forum. "Never take a finished piece from the shop into the house on a sunny day. Sunlight causes scratches." If nothing else, if it is a sunny day, take it outside to look at it for scratches. Been there, done that, more than once. I do wipe my pieces off by hand, or some times use a rag, because the fine dust will go into scratches and some times that highlights them.
I prefer more flexible abrasives to the stiff ones. The edges, especially of the coarser grits can leave scratches. This is more of a problem if you are power sanding bowls and are working on concave surfaces.
robo hippy