A DHTML shell that allows you to query the current browser window. Includes command line JavaScript execution, mouseover DOM query, CSS input, tab completion, profiler and object inspection. Can be configured to run off a bookmarklet, and works in IE, Firefox, Safari and Opera
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.