Ubuntu Software Center not working; says the package catalog needs repair

Try

sudo apt-get update

to update your package list. Then

sudo apt-get autoclean

to clean up any partial packages. Then

sudo apt-get clean

to clean up the apt cache.

sudo apt-get autoremove

will clean up any unneeded dependencies. If while doing this you can identify the broken package this code will very forcefully remove it.

sudo dpkg --remove -force --force-remove-reinstreq package name

Change package name to the real name of course.