Simple problem: Every time I move a note in the Piano Roll, Sonar MOVES it, but it leaves a copy in the place of the old one. Is there a setting to disable this?

Are you by any chance pressing CTRL while dragging, or perhaps your mouse's Right-Click needs cleaning?
 
Mel

Or do you have another track with the same notes showing in the PRV?
 

OTNC, I must be an idiot. I'm really getting used to the controls in 3DS Max in which you hold control to move around the workspace. For some reason I was getting the impression that pressing CTRL retained the measure location while just changing the pitch.
I though wrong! Haha, thanks a bunch!

You'll want Shift+Click for that one...