DigitalDust ScottB9 Please post a dxdiag so I can see what hardware and drivers you have installed. Click Windows key-R, enter dxdiag in the run box, wait for the scan to finish, click "Save all information," and save the file to your desktop. From there, you can attach it to a reply using the paper clip (Attachment) icon included with the other formatting buttons.
You can also try disabling Edge Smoothing in-game and using your graphics control software to apply anti-aliasing. If you don't know how to do this, I can describe it, but I need to know what GPU you have.
ScottB9 Are you saying that some objects cast these shadows no matter what? Or does replacing the items, or placing them elsewhere, fix the issue?