Sorry Brad, I thought I responded to this a long time ago, but when I came to check for your response, my comments were not there. To answer your question: "What information specifically are you hoping to be notified about?"
I would like to know when content has been modified in the LMS so I can update my DB.
It is probably overkill to include submission data in that, but for modules and assignments and other content it would be useful to know if there was a change.
Perhaps most important is being notified that a course has been copied. We are putting a ton of effort into settings for a specific course, but when a course is copied from one semester to another, the LTI configuration carries over, but all of my settings for that instance of the LTI have to be reproduced. If I were notified when a course was copied, with the id of the new course, I could duplicate all of my settings as well and save the instructor dozens of hours of redesign.