We have an e-commerce site that uses certificates from Thawte, we had our certficate renewed in October. If you access https-pages from IE6 you get a warning that the certificate has expired, if you look at the expiration date it's actually the old certificate. Now, this doesn't happen at all when accessing the page from IE7.
This happens when accessing the page from ANY computer with IE6 so it can't be that the certificate is cached locally.