ive had moire pattern like this with old magazines with images using half tone patterns - try a piece of black card behind scanned paper and test if does this on other scanner - i have used photographs of art instead - if careful is okcould also scan photocopies - there are special scanners to avoid this but we didnt get good results
Moire effects like this are caused when two regular patterns interrupt each other — in this case, the pixel grid of the digital image and the half-tone pattern of the original. Generally what that means is the the resolution you're scanning at it too close to the lpi of the halftone screen. If you increase scan resolution so that each individual dot is distinct, you should avoid the moire. Lowering resolution might also work, but I wouldn't recommend it; better to scan in high-rez and then resample in Photoshop or similar.Another thing to try is to angle the original on the scanner platen. This can reduce or eliminate moire effects because the two grids are no longer at a similar angle to each other.Alternately, check if your scan software has a "Descreen" mode, though this can result in a softer scan overall.
Another thing: if you're scanning greyscale or black-and-white images, scan in greyscale mode. It'll reduce file size markedly, even if you use a 16-bit greyscale format for extra dynamic range.