Recently my Logitech MX Revolution mouse got sick: the mouse button started sending multiple clicks instead of just one. Fixing it was conceptually simple: just replace a microswitch. The practice was mildly more difficult.
This isn't a step-by-step guide. It's just a note of the things I'd have liked to have known before I started. Proceed at your own risk!
Opening the beast.
You'll need to peel away the low-friction pads on the base. This reveals some small screws which, when undone allow the mouse to come apart. I was moderately careful when removing the pads, and they've gone back on the mouse without any problems. You only need to remove the big pad at the top of the mouse, and the two small pads at the bottom.
Once apart there's the usual routine of undoing some more screws, disconnecting cables and so on. To get the PCB away from the base (which you'll need to do if you want to replace the microswitch), you'll need to desolder the connections to the charging points.
A replacement microswitch.
The switches for the two main buttons have part number D2FC-F-7N, which a little Googling suggests is made by Omron, and used in quite a number of Logitech and Microsoft mice.
I couldn't find an supplier of these, but if you're in the UK Rapid Electronics part 78-067 works perfectly well and costs a mere 13 pence (plus VAT). Outside the UK you might find the data sheet more useful.
Jehan emailed me about this saying:
I had the same problem with a sony vaio mouse (manuf. by Logitech). I fixed mine by actually opening the tiny switch with a very tiny screwdriver and cleaned the contacts inside the housing!
He also found someone else who'd worked this out.