Later, for a laugh, I decided to try the Wii's browser (which is based on Opera). After persuading it to connect to the webmail address (hint: if you want to connect to a non-standard port, you have to enter the full URL including the "http://" bit) I then entered my username and password and selected the login button. At which point everything on the page disappeared except for the background image. I suppose this is a slight improvement on the Kindle. Actually if you then reload the page it seems to work, but I only tripped across that by accident when hitting the Wii browser's "change layout" button.
It's all shiny and AJAXy and Web 2.0 and completely pointless, not to mention broken in at least two web browsers. What was wrong with just using a server-side redirect (like the previous version did)? For that matter, what was wrong with using HTTP-based authentication (like the version before did)?
Oh, and in Internet Explorer 8 the background image on the login page doesn't show up. That's not due to a browser bug, but rather it's a deliberate decision in the CSS.