I originally filed this as an upstream bug here: https://bugzilla.gnome.org/show_bug.cgi?id=708846 In F20 I am observing log messages below the password dialog. This looks broken for a few reasons - there isn't time to read the messages, and they are ellipsized to the point where the full message isn't displayed anyway. We need a properly designed solution for this, and that's something we can work on for F21. In the mean time it would be good to disable the lastlog messages from showing in GDM.
pam-1.1.8-1.fc20 has been submitted as an update for Fedora 20. https://admin.fedoraproject.org/updates/pam-1.1.8-1.fc20
Package pam-1.1.8-1.fc20: * should fix your issue, * was pushed to the Fedora 20 testing repository, * should be available at your local mirror within two days. Update it with: # su -c 'yum update --enablerepo=updates-testing pam-1.1.8-1.fc20' as soon as you are able to. Please go to the following url: https://admin.fedoraproject.org/updates/FEDORA-2013-19083/pam-1.1.8-1.fc20 then log in and leave karma (feedback).
pam-1.1.8-1.fc20 has been pushed to the Fedora 20 stable repository. If problems still persist, please make note of it in this bug report.