The site uses Qunit and TestSwarm module to automate all QUnit tests. To start the automated testing, go to QUnit tests for the current browser, if your browser didn't do any tests before it should automatically start doing all tests for all themes, otherwise you can start all tests at once. Once finished you should see a color-coded table indicating the status of each test.
A general overview of all test and their results can be found at Overview of QUnit tests including links to the detailed test results.
A lot of thanks to BrowserStack for letting us test their API.