When you print a document with screen shots, moiré patterns may appear in any area that is composed of a tiny pixel-by-pixel, or sufficiently small checkerboard pattern. You will find this most often in the area above and below (or left and right) of the drag handle of a Windows scroll bar. Such patterns are very hard to print without moirés.
The scroll bars (not the drag handles) are composed of a combination of two colors, called ScrollBar and ButtonHilight. (By the way, I've done this only in Windows 2000.)
Unfortunately, you can't change ScrollBar and ButtonHilight using the Display control panel; you have edit the registry. The settings are located in HKEY_CURRENT_USER\Control Panel\Colors.
I typically set both of these colors to "224 224 224", which is light gray.
If you want to go back to the defaults, ScrollBar is 212 208 200 and ButtonHilight is 255 255 255.
And note also that logging off and on may not be sufficient to get them to stick -- you may have to reboot.
Another way, but perhaps no less painful, is to work with screen angles to force the black to print at 0 degrees. If you do it for the whole job, depending on the rest of the document (whether it has any color or the nature of the other graphics), the outcome could look generally worse - but you'll have nice scroll bars!
You could also force the angle in each screen shot and use EPSs.