Um, so not exactly an overwhelming response.
I have now moved my site to the root folder of the domain, whereas it was previously in a sub folder and have upgraded to WordPress 3.3.1 and Absolum 1.1.5. One of these actions or possibly something else has solved the problem and the slideshow works.
I spoke too soon here. The slideshow works now but the customer header doesn’t.
When I select a new header image from my local hard drive and click the upload button WP returns to the Manage Themes page without uploading anything. I have tried reverting to Absolum 1.1.1 and reinstalling WordPress 3.3.1
Disheartening. I’m very glad I didn’t donate!