Sounds like you are describing moire, which is common when scanning printed materials. There's a wealth of information available on dealing with moire. Often if you just ignore it, prints look OK.
The easiest way to prevent moire is to use a scanner setting called "de-screen". If it persists, scan at 300DPI, then re-sample the image to 150DPI in Photoshop. That usually eliminates it, but in the worst cases you can also use a noise reduction filter to soften it.