I added a new OpenID recently and I lost all my interesting tags. None of them are to be seen in my profile or home page.
I also lost my recently awarded Pundit badge momentarily, but right now I've got it back. And I keep earning an abnormally high number of new Good Answer and Nice Answer badges, which I suspect I actually had before - I can't remember.
I would have assumed that logging in with a different OpenId would just give me access to exactly the same data, only through a second entry point. Instead of adding a second door to my house, now I see that some furniture has been changed.
Update. It looks like I created a second profile which later the system merged with incomplete data from the first one. I must say the whole process is looks highly counter intuitive to me (I just wanted a second way to log in to my existing profile), but it may be forced by the specific implementation.