In my experience certain browsers (especially if outdated) have a problem with the interface.
My Google Chrome for example has your same problem along with a charming tendency to ignore the log out button (in both cases of logging out or character switching it merely reloads the page).
My solution was (since I am far too lazy to clear cookies to see if this solves the problem) to simply use a different browser, or more commonly just open a "Open New Incognito Window" using the wrench symbol and log in from there.
