It will come as no shock to any Web developer that IE6 chokes on its own vomit given the slightest provocation, even with a well-tested, cross-browser library such as jQuery UI.
In this case, it was setting the 'modal' property of the jQuery UI dialog to 'true.' Commenting out that line made everything all better. That's all for now. Watch for other random bits of tech and other gibberish from me in the near future.