First let me start of by saying this problem occurs both in Firefox and IE. Second, I've spent a considerable amount of time trying to find an answer to my problem in the support forums. Most of the problems I see are very old dating back to WordPress 1.2. I currently have 1.5.2.
I am logged in my admin account for wordpress, and my comments.php page is set so that it should show "Logged in as admin. Logout." and the regular comments form when I'm logged out. In firefox it always shows me as logged out. Although, I can type in the comments box without putting name/e-mail/url and it sends the comment as if I'm logged in (which I am).
I was trying to figure out what was wrong, so I opened IE to test things. I logged in using IE and went to one of my posts to post a comment. In IE now it always shows "Logged in as admin. Logout." even if I've already logged out. If I were to attempt to write a comment while being logged out (yet seeming to be logged in) it would say that I'm missing name/e-mail/url information.
In addition to this, I need to explicitly go to the wp-admin interface in order to logout. WordPress won't allow me to logout successfully in individual comment pages where it says "Logged in as admin. Logout." It will act like it's logging me out and redirect to the login page, but it won't actually remove the cookie.