According to the article, they lack crucial features such as double-blinding. Most social networks lack the openness and data retention critical for effective peer review. It is possible to learn something from a network like the one described, but I would hesitate to call it science.
Lack of double-blinding ought to increase the false positive rate, right? But the result presented in the OP (the lithium) was a finding of a negative.
When you're suffering from a life-changing illness, where do you find information about its likely progression? How do you decide among treatment options?
You don't want to rely on studies in medical journals because their conclusion-drawing methodologies are haphazard. You'll be better off getting your prognosis and treatment decisions from a social networking site: PatientsLikeMe.com.
PatientsLikeMe.com lets patients with similar illnesses compare symptoms, treatments and outcomes. As Jamie Heywood at TEDMED 2009 explains, this represents an enormous leap forward in the scope and methodology of clinical trials. I highly recommend his excellent talk, and I will paraphrase part of it below.