All I'll say here is that it's not entirely apparent that craigslist is immune from liability because of the CDA:

http://www.ca7.uscourts.gov/fdocs/docs.fwx?submit=rss_sho...

That case, the one I believe most people are citing when they use the words "common carrier" in conjunction with craigslist, was about an advocacy group targeting craigslist for allowing discriminatory rental housing ads. "Go sue the people posting the ads", it said. But note also this, from the opinion:

Nothing in the service craigslist offers induces anyone to post any particular listing or express a preference for discrimination; for example, craigslist does not offer a lower price to people who include discriminatory statements in their postings.

This is clearly true for rental ads, where craigslist provides a forum for a huge variety of different real estate ads, most legitimate, in which it is prohibitively difficult for craigslist to isolate the offensive ads. It is not as clearly true for the "adult services" ads, where craigslist has gone out of its way to segregate the ads most likely to violate state pandering and prostitution laws.