So at the top of each template you will see "tv" - Tag Version and "tc" - Tag Comment.
The Tag Comment will tell you what was the most recent change to the template. We are currently building a release notification system for tags, so that you can see when tags have been added / changed.
Also of note some of the more popular templates, do have articles on the TLC, which you can read when an update is done.
As for being able to do a diff on your current template and the latest version, that is a very good idea, one which I have been meaning to implement. I will co-ordinate with Development team to see if we can get this released.
Please remember to mark solutions as accepted for future searchers.