Hi Niklas,
>can you scan them again, but this time in black and white mode? (not colour nor grey scale, simply black and white).
>This should bring the document size down to less than 1MB and those grey spots will disappear
If you use have some picture processing software like MS Photo, Adobe Photoshop or Corel Whatever available, scanning in greyscale mode actually is a good idea.
The trick to get clear pictures simply is to adjust the "gamma factor" slider towards a lighter image to bleach the grey areas to pure white without getting the ragged-edge fax look of plain b/w.
In my experience, a greyscale JPG with high compression factor looks better than a pure b/w picture and isn't that much bigger.
That's for single pages, though - I don't know how the Adobe software you're using works in detail, but I have great faith in Adobe in general! :-)
Regards,
Henning (HoHun)