There was an excellent hint to solve the Java-crashes in Mozilla 1.1 on one of the discussion-boards in Germany:
- Download MRJPluginCarbon-1.0.1 (make sure you get the OS X version)
- Open the folder and copy the MRJPlugInCarbon to /Library -> Internet Plug-Ins and/or ~/Library -> Internet Plug-Ins
- Now for the new part: Control click on Mozilla 1.1, select Show Package-contents, drill down to Contents -> MacOS -> Plug-Ins, and replace the MRJPlugin with the new version. Mozilla must not be running when you do this step.