I have been following this topic for a while and looks like it is definitively a Hardware problem with some added Driver/Software issues. That is, if set up correctly, you will not suffer from the faulty switches.
I have the following setup:
iCue: 4.19.191
Mouse Firmware: 0.5.64
Dongle Firmware: 0.5.59
I do not suffer from double clicking on either left or right switches. Looks like the iCue is a non-issue and I'd definitely recommend to downgrade your Mouse and Dongle Firmware. However, it is not the only way people have found a workaround the problem. So, if you are experiencing double clicking in this mouse, I recommend trying at least one of the 3 following solutions:
1. The easiest way looks like disabling the multiple HID drivers. Go to Device Manager and disable all the Mouse HID drivers as possible (that is, if you disable the driver and the mouse works, keep it disabled).
2. The second easiest is to downgrade the Firmware (like I did). You can download these versions from this thread on the same topic. A post by "SlugMan" has a dropbox with the files.
3. Change the crappy Omron switches. Though for this you need some tools, seems to be the best way to solve the issue, and you get a nice upgrade in the process. I will do this eventually so I can update the Firmwares (currently versions 5.xx.xx are available, so very much ahead of what I have).
I hope this is useful.