He's mentioned the standbys like Selenium and Firebug, but he also covered Crosscheck. I'll just quote from their website.
Crosscheck is an open source testing framework for verifying your in-browser javascript. It helps you ensure that your code will run in many different browsers such as Internet Explorer and Firefox, but without needing installations of those browsers. The only thing you need is a Java Virtual Machine.
Apparently it's much faster than trying to run in every browser and catches a lot of the big problems right away.