Just want to throw it out there. I don't think signing the back of your license is valid any more (at least in BC, if not Canada). You actually need to register through BC Transplant (or where ever you live).
My friend works for BC Transplant and recently put a link of facebook about signing up. It just linked you to the Transplant website where you signed up as normal... If you don't want it on facebook that you're a donor, then just go to the site directly.
In AB you can still sign the back of your health card (ours are just a flimsy piece of paper).
This is an interesting topic for my family. DH is going to be a living kidney donor in a few weeks. It has been a year long process full of testing, testing, and more testing. I have a heart on my drivers licence that signifies that I am a donor. I am not sure that it is necessary to do that and FB, but I see nothing bad that could come of more awareness.
The only problem I could see would be someone who impersonated someone else on FB and signed them up if they were actually not willing. I doubt this would be very common though.