Given a centralized wiki, what is the best way to track changes? What does wikipedia.org use?
All versions of a wiki article are recorded by the MediaWiki software used to host the various Wikipedias. Just look at the History link on any page to see the list of versions.
The MediaWiki software itself is composed of different sub-systems which are tracked via various systems - the main source is viewable at https://phabricator.wikimedia.org/source/mediawiki/
Bug reports and change requests are managed on Phabricator at https://phabricator.wikimedia.org/
Some developer information is at https://www.mediawiki.org/wiki/How_to_contribute