All the credit goes to Paulo Matos who carefully worked out and tested this fix, and updated the patch several times over more than a year while I very slowly got around to reviewing it and checking it in.
* Don't let the user set the name for random questions.
* Instead force the name to be "Random (catname)" (localised) whever the question is created or saved.
* When a category is renamed, rename all the random questions in it.
* Remove the restriction that Jamie seems to have added in 1.9 that was preventing the category of random questions from being edited.
If there are any of the files styles.css, styles.php, script.js or script.php in the plugin folder, they will be linked to in the head of the quiz attempt page (only for the question types used on that page).
If you need to do something more complicated in your question type, you can override the get_html_head_contributions method instead.
While implementing this, I removed the ~100 lines of very similar code from the top of each question type's editquestion.html template, and moved this to a the function print_question_form_start() in the base class, which uses the template question/type/editquestionstart.html. This is described in more detail here: http://moodle.org/mod/forum/discuss.php?d=51590, and is why this patch makes the codebase 523 lines smaller.
tjhunt