So admittedly, this answer isn’t going to help most of you that have encountered this. Unless you happen to fall within that 1% that, like me, have a tendency to treat their mac a bit more like a linux box.
In my particular case, I had been messing with the sudoers file.. Effectively I had gotten the syntax right, but I had inadvertently limited the %wheel% group to just one command.. so visudo was happy to save the file for me, but once the damage was done there was no going back.
In the past I had run into a similar problem, and the answer was to open the Finder, go to the /etc folder, and modify the permissions on /etc/sudoers so that I could edit it. However since Mavericks, this does not seem to be possible. Now whenever I tried to do anything that required elevated privileges I would click the lock button and then encounter that dreadful error message, “Unapproved Caller: SecurityAgent may only be invoked by Apple”. How terribly unhelpful.
After much googling I realized that I was never going to find a workaround while the box was online, so I simply rebooted it into single user mode (apple-S on startup), and then manually fixed the sudoers file. Problem solved.