I’m having the same issue, but here’s some more detail on how mine comes about:
It started when I tried to set the URL for WordPress to a different URL (one that is redirected) than the folder where WP is installed. For example, the blog is installed at http://www.mysite.com/wordpress but I set it to http://www.cooldomain.com. I’ve also, of course, set http://www.cooldomain.com to redirect to http://www.mysite/com/wordpress.
When the setting takes hold, I cannot log in to WP and the extra slashes start appearing. Some details:
Hopeful this clarifies the situation. If my problem is completely separate, please let me know and I’ll start a new thread.