I think this needs to be a full plugin, because the Google API needs a key to use. Otherwise, it blocks you after a certain number of tries. But, yes, it's basically a script to check and report.
I don't know where it needs to be. Ideally, I'd like to check new links when cron runs, but I don't know how to make sure that gets reported. Then I'd like to have the opportunity to do a scheduled run and report- weekly should be fine. It needs to throw away links that are dupes, and bad links. And then it needs to list as you said, along with course name & number.
I think I had about 30% dupes in the URL list, and probably about 50% near dupes, fyi
Off to get an API key, for today's work.