Hi Bryan, thanks for getting back to me. It's mysteriouser and mysteriouser. Yesterday (24.9.12) I used MS Fixit which clears almost everything except the kitchen sink it seems but it made no difference at all. (Not even after I rebooted).
But today, lo! My slide shows are back working properly. Very strange.
I've cleaned out the cache and cookies again just to be sure, but this is something I do regularly anyway (routine maintenance).
I still have the other problem that I think is connected somehow which is that some sites including don't recognise that I have the latest version of IE9 installed & kept updated. For example, if I visit http://www.independent.co.uk/arts-entertainment/books/features/the-bionic-book-worm-8168123.html for example, I get an error message if I try to comment. It says, Sorry, the browser you are using is not currently supported. To use the comments, Disqus recommends the following browsers:Firefox Chrome Internet Explorer 9 Safari. And IE 9 is what I'm using.
For ages, I've been getting WP reminders to upgrade to IE9 or I won't receive notifications, when I've had IE9 all along. For most of the past fortnight, my stats haven't loaded in IE9 but load ok in Safari. It's very puzzling.