Disable expanding scroll bars in Mountain Lion
In "System Preferences > General" There are three options for "Showing scroll bars". From your description, it sounds like you have the default settings of "Automatically based on mouse or trackpad"



You may find "When Scrolling" or "Always" more to your liking. I'm an old school Mac user, so I have it set to always. That setting solves this problem and other scrolling problems. 

If scroll bars were meant to be hidden, then Andy Hertzfeld would have written them that way in the first place.