We've seen many client networking issues that would be much easier to debug if there was an easy way to test connectivity between all nodes. Common examples of failure conditions include over-restrictive firewalls and misconfigured DNS or /etc/hosts.conf.
It would be nice to be able to run a command on mongos that will gather up all "important" hosts in the cluster (all config servers, all non-hidden members of all shards), then have everyone test connecting to everyone else. The output would be an N*N matrix that will show any potential networking issues. Ideally this could use the _isSelf command or something similar to make sure that everyone agrees about which server "host1234" is.