Here's the setup:

Early 2007 MBP 15" with broken display
Samsung 20" LCD
Apple Bluetooth keyboard
USB Logitech Laser wireless mouse
OSX 10.7 (Lion) + all updates

After the display died a few years ago, I basically turned it into a Mac Mini

A couple of weeks ago, the left mouse button stopped working when clicked. The right button still works, and it still tracks around the screen. The only fix is to do a hard reboot. After the reboot, everything is fine for a few hours, even a few days. Then it's back to the left button not working again/

I've tried using the other USB port, same result
I plugged in a USB hub, same result
I grabbed another mouse (same model), same result

I am looking for any hints or thoughts on what I should try next.

Cheers,

i would first try with a known good wired USB mouse. if the problem persists i would look at the IR receiver (assuming that mouse has one). if it persists after that then i would probably try booting from another known good OS (i.e. OS on an external drive or target disk mode etc)