Okay I think I was able to recreate what you're talking about.

Here is "my" take on what might be happening (just a guess, have not verified or tested theory)

When you log out you don't actually delete the cookie but maybe just alter the data in the cookie to be noticed as logged out.
However posts status read etc is still being updated in the cookie so when you log back in the read/unread is not correct.

IF that is what's happening or if it's cache/cookie mixture of issue then I would suggest that when you log out that the software actually delete the cookie and not just modify it, or create and use a DIFFERENT cookie for logged in vs not logged in.

Without looking I think there is different areas that are tracked some by cookie, some by DB but yes Mark I agree with you that it should not operate the way it currently does.

I rarely browse not logged in so did not notice it, but agree it's not done properly (IMHO).