Q: magic mouse very erratic on new iMac computer

The wireless magic mouse that I got with my brand new iMac using mountain lion OS acts very erratic. I shut of all features except right and lift clicking and vertical scrolling, but it didn't help. When I try to click, some times it works and other times it does not. Right clicking is worse than left clicking. Sometimes, the screen will just scroll when I don't even have my hand on the mouse.  Took yhe mouse into the apple store, and they claim it is OK.  I am now using a Logitech M310 and it seems to work much better, but it uses up one of my USB ports. Any suggestions including a substitude mouse which does not use a USB port.