I disagree with Glenn. Rule out hardware problems, especially issues with the KVM switch and its cabling, before touching the OS.

Replace and/or swap out and/or try:

-keyboard
-mouse
-every KVM cable including video and mouse and keyboard
-ports on KVM switch
-KVM switch itself
-direct plugin without KVM switch
-unplug all other peripherals including all USB devices
-pull cards out of the computer (if any) until you're down to just the video and the keyboard/mouse

Do all of the above before trying to reformat the computer.

Reason: Your description sounds like problems I've had in the past which were always hardware and cabling related. Driver problems are all well and good, but I've never seen a bad driver cause ghost mouse clicks.