I usually prefer to fix a Linux system than to reinstall from scratch. My computers have seen many distribution upgrades and a list of PPAs or third-party repositories. APT usually makes sure that everything works in the end. However, the fact that the package manager thinks that all required packages are 'installed' does not guarantee that all the files are present on the file system.

Such a such situation may occur if you have to work-around dependency problems with dpkg --force-*. One could also reproduce such a situation by deleting a file from /usr as root.

Is there a simple way to verify whether all files belonging to an installed package are present?

If a such a problem package is found, aptitude reinstall fixes the problem.