If you have some spots that are through the finish into the wood, I'd suggest thourghly clean the floor, get some stain the color of the floor, lightly sand the area, apply the stain, then apply finish. It won't match perfect, but the only way to do that will require a total sanding and refinish of the floor. I wouldn't paint, if you ever want to refinish to natural wood tones it will make the job harder to do.
Just my