How to grant sudo rights only to specific script files?
I think you are almost there. put a / at the end of your directory spec
jsmith ALL=(ALL) NOPASSWD: /usr/local/tomcat7/bin/
From the sudoers man page
A directory is a fully qualified path name ending in a '/'. When you specify a directory in a Cmnd_List, the user will be able to run any file within that directory (but not in any subdirectories therein).
Add a slash '/' to the end of the path.
jsmith ALL=(ALL) NOPASSWD: /usr/local/tomcat7/bin/