When editing a script that uses the Courier New font, you can sometime see drawing artifacts (parts of lines, text) appear beneath the line you are editing. Sometimes, at specific magnifications, you can cause these artifacts to happen when you scroll.
There are two solutions: the first is to use Courier MM Screenwriter, which has been fine-tuned for one-screen editing and also looks better when printed. Usually, switching over to Courier MM Screenwriter is enough to make these artifacts disappear.
The other solution involves making sure your zoom magnification isn't set too low. Try a magnification above 150% and see if that helps.