Ask HN: how do you regression test your web apps?

In working on Skulpt (.org) I'm growing a decent sized JavaScript code base. I have reasonable test coverage running on d8 (the V8 debug shell) and can run the tests quickly (< 10s) from the command line.

There's a minimal amount of DOM stuff in demo code that's entirely untested, and more importantly for this project, various levels of support and quirks in the browsers' JavaScript implementations that affects the core code.

Assuming a Linux dev environment (though I've got at least 4 XP licenses for VMs if necessary), my question:

How can I set up an unattended process (i.e. one command) that can reliably and quickly tell me whether everything's working on ie7, ie8, ff2, ff3, safari3, safari4, opera9, opera10, and chrome? (x OSs as appropriate)