On my home wifi network, my nexus 7 has a connection and I can browse and download apps, but can't log into facebook and just get the "no connection" error. Try removing Facebook app then install it again, cleaning the cache and not working. I can access FB on my computer with no problem.
However, when I try logging into a public wifi hotspots, facebook works fine on the tablet. After swicthing to home, it just won't work again. Finally, I go to flush my router/wifi, renew the IP and then fix the issues.