A few people seem to be bitten by an error in the Ubuntu distribution of Tomcat7. Basically when you shut down the service it gives the following messages:
Opinions differ on what causes it, but it is pretty clear: Tomcat is assuming that the shared, server and common directories, which are in /var/lib/tomcat7 are in /usr/share/tomcat7. In other words, the configuration has mixed up catalina.home with catalina.base. catalina.base is supposed to be /var/lib/tomcat7 and catalina.home is /usr/share/tomcat7. All you have to do is edit the file /var/lib/tomcat7/conf/catalina.properties so that all references to those directories have the correct prefix and you're good. I ignored the "common.loader" line as changing this created some weird effects. But lower down the file is mixed up. Reboot and you should be good.