a lots of (Permission denied) in catalina.out

Can't vouch for the security of doing so, but

$ cd /usr/local/tomcat/ #or /usr/shared/tomcat6, whatever your $TOMCAT_BASE dir
$ chown -R tomcat6 webapps temp logs work conf
$ chmod -R 777 webapps temp logs work conf

works a treat for these situations.

My tomcat install was borked with permission errors, but throwing open the gates thusly fixed everything.

$ chmod -R 777 webapps temp logs work conf

Is VERY dangerous, do not do it, did I write "not do it" ? DO NOT DO IT! Guess where your tomcat-users.xml is with your usernames and plain-text passwords ?

Giving world read-write-execute anywhere on UNIX except /tmp (and even then, in prod, NEVER do that either) is plain stupid. And, it makes your first line, chown -R tomcat6 completely useless.

make sure tomcat runs as tomcat7 (it is tomcat6 for tomcat 6) and simply do:

$ cd $TOMCAT_BASE
$ chown -R tomcat7:tomcat7 webapps temp logs work conf
$ chmod -R 660 webapps temp logs work conf

[EDIT] changed 770 to 660 following comment, because the files in question need not be executed.

If you want to be able to read, write, or execute stuff there, add yourself to the tomcat7 group.