BBC iPlayer renders weirdly

Using the HTTPS Everywhere plugin on the site www.bbc.co.uk/iplayer causes the site to render badly. I believe that this is a bug in the BBC handling of the request but it appears that the site should be added to a whitelist.

N.B. I believe that the BBC uses GeoIP locating to differentiate between UK and non-UK addresses so different results may be found when testing this from outside the UK.