That's just how dithering is.
You could try to scan in grayscale, and have the printer do the dithering (see Printer properties, choose B&W instead of color), but I doubt it makes much difference whether the dithering is done by the scanner (or scanner driver), imaging software, or printer (driver). But this way, you can keep quality images for filing.
I generally scan documents for archival at 8-bit, 300dpi with very good results.
Hossenfeffer,
I'm not a scanning expert, but wouldn't you want to scan at the highest quality settings possible? If you're scanning the proofs, you can do 24-bit, 600dpi (or 1200dpi for many scanners) and output to TIFF instead of JPEG. Realize each image will be quite slow. I believe technically, scanners are 48-bit, but the output image is 24-bit aka TrueColor.
I have even less knowledge of negatives, but I seriously doubt any SOHO negative scanners will be any good for archival scanning. Is it feasible/affordable to rent a quality (commercial) unit for the job?*
I think the best option here is to get Kodak
PhotoCD. Note I learned not so long ago that Kodak
Picture CD is a low-grade, consumer option. I don't remember exactly, but image resolutions for Picture CD are approx. 800x600. PhotoCD is significantly higher. If your studio doesn't offer PhotoCD, I can't imagine why you couldn't take the negatives to a shop that would cut you PhotoCD disks at a reasonable price. It'll save you a lot of effort compared to scanning it yourself.
As for Picture CD, it's fairly low-res, but still worth the $5 you spend, considering the time saved scanning prints for all but the most important occasions. The JPEGs are more than adequate for web images.
*For example, the following film scanner is almost $2 Gs.
http://www.microtekusa.com/as120tf.html