Periodically audit file permissions for mistaken leaks

I'm looking for a way to periodically check a file system tree for permissions that have been set incorrectly.

The context is:

• this is in an academic compute environment, with students, researchers and overworked sysadmins
• the focus is not on malicious actors, but rather mistakes made by any of the above
• existing users/group hierarchy
• prevention does not have to be immediate, we're thinking of something that can run daily
• ideally don't want to have to install extra tools such as tripwire
• don't need a forensic trail to be captured

My hunch is a script that:

• runs daily via cron
• runs as a user with read permissions for the entire tree
• checks that rwx is off for the "all" bits.. (more rules to be added)

Before I start this, is there an established way to do this that I'm not aware of?

You want to check AIDE or mtree

More generic list of File integrity monitoring software