So, I'm bringing this one back up. I've tested under WP 2.3.2 with two different browsers and two different blogs. General info: Mac OS 10.5.1; I'd've have to look up the PHP and MsSQL.
==> Under Safari 3.04 with blogA and blogB, I quite literally cannot log off; I can see the post-data 'logout="true"' flash by on the toolbar location window, but I'm just returned to the dashboard. Because I can't get to the login screen, I can't determine the status of the keep-me-logged-on checkbox.
==> Under Firefox 126.96.36.199, when I click the logout (sign out) link, I'm dumped back to the login window, but both the userid and the password fields are completed correctly. The keep-me-logged-on checkbox is not checked. When I log in as a different user and then log out, dumped back to the login window, but both the userid and the password fields are completed as the admin user with the admin user's password.
Does that look like a security problem?
I'll toss cookies (not the kind I tossed when I was a lot younger!) and then I'll test again. Also, I'll test on a different box soon.