I recently had this issue, with both the Forward and Back buttons not working, and either having to restart iCue or in some cases reboot the computer! I found that mapping them to Forward and Back in the iCue software (even though that's their default function) seemed to solve it. I've not (yet) had the Left-click problem but I'm wondering if that's worth trying (mapping it to Left-click in iCue)?
Quite often I'll also find that the mouse isn't detected, either at boot or waking from sleep: fixed by unplugging/replugging or killing iCue.
I've only recently come back to Corsair, having bought a K70 Mk.2 SE, and am remembering too late that iCue was the reason I went elsewhere in the first place!
Now my scroll wheel is starting to wear out and after reading this thread I'm pretty sure I won't be getting another M65. Shame, because it's a really comfortable fit for my hand.