I did a little more digging. It definitely works fine on IE7 and on IE8. And eventually I got it to work on IE6.
If I go directly into roundcube, the first time, it does not work. I close the browser and try again, same result.
However, if I go into roundcube and keep the broken page up and press the refresh button, the roundcube screen renders correctly. So, it has to something to do with the initial build of the page.
If I exit IE6 now and go back into IE6 and go to roundcube, everything works fine. However, if I delete the IE6 cache and then go back in, the same problem occurs.
I have attached screen shots of the results.
What ever is causing the problem really flakes IE6 out, because it won't even let me view the source once it encounters the error.