When you say dashboard header, do you mean the blue bar along the top with the drop down menus? I see it on your blog using IE6.
How long ago did you map this domain? I noticed that it too a few hours to work fully for me on mine.
I know TinyMCE got upgraded a couple of days ago. Since the backend still uses the wp.com domain name, the domain mapping shouldn't be a conflict but you may be hitting the older version of the editor. I know Rain suggested clearing your borwser cache but you stated that you did the refreshing which is two seperate things. if you haven't done so yet, I would try clearing your browser cache. The cookie cache as well.
Are you seeing the regular editor? That's the one with the tabs containing the written HTML code, not the icons.