That's really strange, there's a lot of code in the game to prevent accidental double clicks (as well as Unity's standard input gating). The fact that you're getting multiple clicks with both left and right click indicate that there's something at either the driver or hardware level going on, do you have another mouse you could test with to try and rule that out?
Also, which OS are you playing on with what hardware - if it's Linux we're going to have a hard time tracking down a fix
