We updated our server on 15 January 2015 with the usual updates, but noticed an error afterwards in connection with the package nss-softokn-3.14.3-19. This seemed to be an error one could safely ignore, as the system seemed to run OK afterwards, but as it turned out, it was not.
The new version of nss-softokn was not working properly with nss-softokn-freebl which runs alongside it. That had a variety of effects, but the one that we spotted was that WordPress plugins which rely upon curl stopped working and returned curl error 77. Essentially they could not communicate with outside servers. This was not an obvious problem to solve, but we got there thanks to a very helpful blog post by Linux sysadmin ‘Kite’ on his blog. His thorough instructions (apparently based on a post in the CentOS support forum) did the trick for us, and we are now all back to normal.
UPDATE: a recent update to Centos repositories has fixed this bug directly, so you can now safely update nss-softokn and nss-softokn-freebl with the most recent updates that yum offers, avoiding this issue. But if you have already suffered this bug and yum is not working, you might need to use the fix above before you can use yum again.