WPMU doesn't allow video embed tags in a post by default.
I've coded my own video plugin to insert my own embed tags from youtube, slideshare and teachertube.
If I'm uncomfortable with any video in the future I can pull the plugin and all videos are gone. If no plugin, no video, anywhere.
I use a premium plugin as well, and I enable the plugin for all, but could easily limit access to the plugin if I choose.
I have no trouble going to Blogs under SiteAdmin and suspending a goofy user now and again. Doesn't take long for the offender to come to me sheepishly. Every blog is read by every member of every group during every assigned post.
Any assignment or blog entry is not complete until it has received at least three comments from classmates. Videos must be embeded in context within a post, no context = no post. Therefore, no abuse. Corny vids at times(Bart Simpson=Hamlet), but nothing vile.
Threats work. I have an electric typewriter on a wooden desk next to mine, as well as a desk with dry macaroni, food colour, construction paper, and glue. Their "macaroni blogs" would be posted on the walls, too, if it ever got that far.
If you want to stop images in posts, edit the kses.php in wp-includes and remove the tag and it'll be stripped from posts, too. Every assignment in every class prompts a discussion of hotlinking, fair use, copyright, etc. Properly linked/credited and coded image attributes are in the rubric.
I run the school gallery website, Gallery 2, and WMPU plays nice enough with it via wpg2 plugin. School images, therefore any student images, are all there only. I need only worry about privacy/permission issues in one gallery rather than sprinkled throughout wpmu.