For serious vshare webmasters, this would be a good feature to have, if your site has lots of video content then i think this would be the best way to monitor and maintain your content, making sure everything is playable, so you can keep your users happy, as random user will not always report it but just move on.

this should:
1. check hard copy video files for: video not *found/*access denied/*permission, errors.
2. Crawl thought all embedded videos, finding unresponsive playback.

method of function options to think about:
1. Cron based schedule, with reports in the admin log (but should have it own tab within admin log)
2. Admin panel check now option, (show results after check is complete, just like the process queue function)
3. Mini video scraping to verify playback of embedded videos. (admin should have adjustable input for setting seconds of scrape length time per video, because this can be CPU intensive)

This would be one of the best ways to upkeep the video maintenance of your content.
Also i think their are a few mods that do monitoring of broken embedded code already, i think clip-bucket has a mod like this already as an addon option, i will have to check to be sure. but anyway i think this is a very much needed function for the serious webmaster.