Hi Alastair
I am not a word press expert, but I have similar problems with IE6. Its not just wordpress, but also many CMS that are now in commone use eg the Amnesty UK web site displays fine in Firefox but in IE6 the content drops down and out of sight.
I maintain 3 wordpress blogs and know from the stats that many users are still using IE6 so have got round this by choosing themes that are compatible with IE6, not one written for later versions of browsers.
I cant give you the explanation for this though I am sure you could google it.
So unless you are determined to keep the theme you currently have, I would work you way through those on offer that come close to what you want - although last time I looked the themes directory had done away with the very simple seach function, eg white, 3 column, right hand and its a right pain to do this.
In the end this is what I did although there can still be problems. For instance on this blog http://womensphere.wordpress.com if for instance I put in a very long url it will wrap within the content section and not push them down below the right hand menus. However on this blog http://womensgrid.freecharity.org.uk if I put in a long url it does push the content section down.
I apreciate this isn't a very techie solution, but is a way of dealing with the problem.
Hope that helps
Deborah