I checked out Phil Rosenberg's post  yesterday afternoon about the pros/cons of using LinkedIn and Facebook for your career search. As a recent job searcher attempting to relocate to a new area, I have to admit that I feel both networks do an inadequate at providing solid job leads.
The one advantage to job searching on social networks is that they provide is access to multiple job search databases on one results page. While this service is extremely beneficial to job seekers, the relevancy of the results is often unacceptable.
For example, if you live in an area that isn't heavily populated (say, Western PA outside of Pittsburgh) and you're looking to relocate to another area that isn't a major MSA (Central PA, near State College), many of your leads from LinkedIn are going to be targeted in the "Greater" local area. For State College, that could be anywhere from Harrisburg, PA to Pittsburgh.
Similarly in Facebook, results are heavily driven for each user by network location, and that could dramatically alter the results you see.
For me, using the internet was obviously an important part of the job search process, and so were the social networks. Sites like Facebook and LinkedIn provided a great service to me in seeing job availability in my field, but were no help in actually leading to me landing a job.
Once I found a company of interest in my field, then I was able to discover a job lead and find a make my next career move.