I figured out my issue.  I had set 'Default login cookies length(in minutes)' to 0 so that users would remain logged in forever.  This caused the issue I posted above.  By changing this value to anything besides 0 it resolved the problem.

I just installed 1.3.1.3(smf 1.0.5) and I have the same problem.  Here is what I am seeing:

1) If I login using the mambo login it *does not* log me into smf. 

2) If I logout using mambo it *does* log me out of the smf.

3) If I login using smf it *does* log me into mambo BUT *does not* log me into the forums.  I must login using smf again to be logged into the forums.

4) If I logout using smf it *does* log me out of smf and mambo.

My users currently must login twice, once in mambo and once in smf regardless of where they first attempt to login.

My site is
http://www.themofoclan.com

I have a test user setup:
un:  test_user
pw:  test_user


Thanks for any help.

I thought about starting a new thread for this, but I will try here first.  I installed the latest optional login module (1.3.1a) and have been trying to use it.  However, the logout will not log me out of the forums, it just logs me out of mambo.  Here are the steps

1) Login using the optional login module
2) After successful login, select logout from the optional login module

This displays and error and the pathway changes to home -> upload media
Error states: "You are not authorized to view this resource.  You need to login."  If I look at the optional login module I see that I am still logged into smf but not mambo. 

I went through and deleted all cookies from my site and cleared the cache.  I also verified that my live_site has the www. as suggested previously.  Nothing has worked to resolve this issue.

Things to note:
1) I have the user menu enabled with the mambo logout unpublished.  The reason is so I can have the upload media feature of the zoom media gallery available to registered users.
2) Upload media is the first item on the user menu.  It is not a coincidence that the pathway changes to home -> upload media when I select logout from the optional login module
3) If I select logout from the forum itself I am correctly logged out of both mambo and smf without an issue.