I came across this thread and thought I'd reply with my fix.
My setup: Macbook Pro, Thunderbolt Monitor, Wireless Magic Mouse, Wireless Trackpad, Wacom Tablet
I had exactly the same issue - the mouse and trackpad would move the cursor around the screen, but the left-click function wouldn't work on either device. The Wacom tablet (pen tablet) left click would work. I scratched my head about it, came across this forum, checked my mouse preferences and noticed that there was ANOTHER mouse connected to my Mac. I carry another magic mouse around in my bag for offsite meetings, and the mouse was in range of the mac. The button on the mouse was pressed down by other stuff in my bag, causing a constant left-click signal to be sent to my Mac. I turned the mouse in my bag off and everything is back to normal!
To see if you have other bluetooth devices that could be interfering with your mouse, head to System Preferences > Bluetooth and look to make sure you don't have a conflicting device connected to your computer.