Is there a way to do concurrent editing? Is there a MediaWiki-like method for supporting concurrent editing of text bodies in Drupal 7?

If no feature currently exists, what are some decent PHP diff libraries that could be wrapped up by a Drupal module that could do the job?
You can use etherpad kind of feature which allows you to do concurrent edit of node body.

Etherpad is collaborative editor by which you can write any node field using concurrent editing. Check Readme.txt for installation purpose.

And one more thing if you have no permission to install etherpad on your server(as shared hosting will not allow it) then you can use Piratepad module, which allows you to embed the pad using iframe from piratepad site.