What types of tests—or testing software—could be run on a WordPress site? For example, after we update a plugin on a WordPress site we manually check that the site hasn't changed in appearance. What software – or methodology – would you recommend for automating this game of spot-the-difference?

The nearest I've found (but not tried) are:

Screenster: http://www.creamtec.com/products/screenster/index.html

Wraith: https://github.com/BBC-News/wraith