I'm a little obsessive about my drawing paper. I'm not happy until the borders are spotless, but little bits of graphite, eraser crumbs, and other things manage to find their way there even after I've masked the edges. Sometimes those spots can be tricky to remove. If the speck of stuff is the least little bit oily, dragging an eraser over it can darken it, smudge it, and make it even harder to get rid of.
The next time you find a spot on the paper where it shouldn't be, try following these steps to eliminate it.
1. Before you touch the spot, see if you can blow some of it away with a blow-bulb. (Don't try to blow it away with your breath. You might spit on the paper and cause even more problems. Trust me on this: invest in a blow bulb.)
2. Next, lightly tap the spot with a kneaded eraser that's been pinched into a point. Remove as much of the spot as you can by tapping it, not scrubbing or rubbing. Renew the pinched point often so that you’re working with a clean eraser every few taps.
3. After you've gently lifted as much of the spot as you can with tapping, expose a clean area on the kneaded eraser and lightly stroke it over the area several times.
4. Next, stroke the spot with a clean vinyl eraser. If the spot does not smudge, you can put a lot of pressure on the eraser.
5. If the vinyl eraser doesn't remove the spot to your satisfaction, go over it with a battery powered eraser. (Again, make sure the eraser nib is clean.)
6. If the spot is still there after all that, you can try the extreme measure of "cutting" it out. Put a clean blade in a small Exact-o knife and use the tip to carefully "pick out" the spot. This does leave a tiny mark in the paper so you'll have to decide if you'd rather live with the dark spot or a tiny marred spot. (This maneuver takes practice so try it on a scrap piece of the same paper first.)
A clean border gives your customer lots of framing options, and it looks professional too. Here are some more paper links.