I don't do much scanning myself so I really can't speak from experience :-) However, I've read that it often helps to scan at twice your desired resolution, soften the image a little, and then down-sample the image to one half size in Photoshop. For example, start by scanning at 600 dpi. Next, in Photoshop, apply a slight blur or despeckle filter. Now, down sample the image to one half of the desired pixel size. Lastly, sharpen the image a little using the USM filter. You might give that a try to see if it helps.
Also, I think some scanner software comes with a de-screen filter that is supposed to help. But, I think that filter is for scanning printed material such as magazines etc.
Like I said, I had never actually tried that so I'm glad it worked for you. BTW - In my previous post I should have said "down sample the image to one half of the pixel size" (not half of the desired pixel size). Sorry about that but apparently you understood anyway :-)