Before a semester begins:
Are the needed classes available in Moodle? Are there any you need to have created?
Are there any changes to instructors?
Are there instructors that need to be added to courses so that they can prepare?
Do you have instructors that have never used Moodle? Do they know what the expectations are and where to find help?
Are there new materials to upload? Make sure instructors have lead time to get those set up.
Are there courses that are not used on the server? If there are things that could be cleaned up, pass on that information so it can get done.
During the semester:
Remind instructors to check that their grade book looks like it's calculating properly.
Changes in instructor mean changes in Moodle. Make sure new people have access, and former employees are removed.
Touch base with any concerns and remind them where to get help if they need it.
After a semester ends:
Are instructors to save a copy of grades anywhere? Or submit them? Do they know how to do that?
Remind instructors to clear out students from the Moodle course once the term has ended.
Instructors who are leaving the college should be removed from courses.