With Firefox 3.6 the dynamic loading of scripts is broken, mapbuilder does not recognize Mozilla-browsers correctly anymore.
Obviously document.readyState does now exist in Firefox 3.6 too.
For testing: try to reach the component register:
Thanks to Rober's suggestions I was able to solve the problems (see attached path).
I tested it in IE6, IE7, IE8 and FF2, FF3.5.8 and FF3.6 - it worked fine.