"This usually means that your installed packages have unmet dependencies"
well? it might be right
you can run dpkg (or apt?) to check (various ways, also various softwares/scripts that do this) and find what software has un-met dependancies
it could be that .../lists/... folder has become corrupted (i'm unsure if you can delete it)
if / when you find out what software it has issues with: remove it (and remove all software that depends on it - should be automatic), and re-install. you might need options to ensure "comlete removal" of the packages old files
if picking a fight with packages doesn't work you'll either have to dig "allot deeper" into the issue or re-install (or load a backup. you have one right?
HOWEVER: a quick warning. do you have an auto-updating system? if so, you have to know what version is current and if the problem is temporary - could be you got shipped a bad dependency file or what OR it could be you have a package installed that the new version "had to remove" (yuk) and it didn't completely do so. i could explain how a packaging system, versioning, an dependency system works but it wouldn't matter since the "new maintainers" made it a "closed system": if you can't use commands to ask software to fix the (dependency table) for you: you can't do it.
you should be able to find a way to run the tool by hand, and when you do read the manpage to find the option for "attempt to repair and continue". that might help.
usually, running the tool by hand, many "fixable problems" are noticed and the commandline software asks the Interactive User / terminal user questions to correct certain issues. (so if you haven't - see if there's a commandline tool like 'dpkg(1)' to use)
I'LL WARN YOU - it can be VERY timely trying to fix APT / depends issues once they crop up. It'd be better to load a backup. Or re-install. Or use an iMac and run a linux tools (even X) under mac BSD.
(don't attempt to fix complex apt issues they only get worse)