Take it into Photoshop, and clean it up in there, or play with the live trace settings in Illustrator, or remove the lines after live-tracing.
Probably your best bet is going to be re-tracing the sketch with the pen tool, if it can't be done with live trace and some manual cleanup. You can, by the way, use the magic wand tool to select most of the dots in a couple of tries...
Bert
Here's a quick recap of what you can do:
The first image is a scan of a fake sketch, the second image is a default B&W live trace with Threshold upped until the lines were gone. This may work for you.
For a better result, the Grayscale has "colors" upped to 64, then expanded, the lines deleted a little at a time using the Magic Wand tool. The last image is the resulting vector artwork.
Seems pretty easy to me. Check back if you need more help.
One thing you MUST remember, when using any professional drawing application, is that rarely will you be able to get exactly what you want with the default setting. If there's any advice I could give you, it's FIDDLE.
Bert