Joe Hewitt, in this Dr Dobbs article talks about using the Firebug extensions to inspect and debug Ajax applications (or any browser-based JavaScript application). It also has CSS inspecting capabilities, editing JavaScript on the fly, inspecting HTTP request and responses, logging, breakpoint debugging and profiling. A useful howto.
Svend Tofte puts together a detailed guide to setting up and using the Venkman debugger. From basic debugging to watchlists and call stacks, breakpoints, and more advanced techniques like meta comments and profiling. It also contains a list of other useful Venkman resources.