Here's an easy fix to a very minor problem. Parallels' Coherence mode seems to work, at least on a basic level, by making the Windows OS's background image and other items invisible, showing only the application windows which exist atop it.
This works very well in many circumstances, but when dragging windows around your Mac desktop, you may momentarily see a part of your Windows background image flicker on screen, trailing the window as you drag it. Here's a simple solution that works wonderfully, having entirely eliminated the issue for me: simply use the same background image for your Windows environment as you use for your Mac!
[robg adds: Try as I might, I just couldn't see these ghosts with the latest final release of Parallels (build 3186). However, the author is still seeing the ghosts with the final build, so I thought it worth sharing his fix.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20070224122035668