Raising the threshold/lowering sensitivity settings on the triggers helped eliminate a lot of the random overhits. I still get occasional ones on yellow cymbal when doing fast sixteenth notes. There's a screen you can get to that will show what is getting registered as you play (in the form of vertical bars), so you can tweak your settings outside the game and make sure you're not getting more bars than hits.
Expert Pro Keys: 50/63 GS, most recent The Killing Moon
Expert Pro Drums: 53/83 GS, most recent Free Bird / Oh My God / Oye Mi Amor
Expert Pro Bass: 6/83 GS, most recent Everybody Wants to Rule the World