this post began with a problem I had and managed to solve before posting. Since the domain mapping support pages don't mention this (and I think they really should) I will post this anyway in the hope it helps people encountering the same problem.
Situation: You have a wordpress.com blog succesfully mapped to a subdomain you own. (I don't know for sure it happens also with full domain mapping, but it could).
Problem: When you go to your blog and try to log in, you are redirected to the wordpress.com dashboard. There, everything works fine, but when you try to actually browse your blog at your own subdomain, you mysteriously appear as logged out. Whatever you do, you can't login unless you are in the wordpress.com domain, and then your blog refuses to take notice.
Cause: You have disabled third party cookies in your browser (or firewall or whatever). Thus, your log in is only valid under the wordpress.com domain, not your own subdomain.
Solution: The only solution is allowing third party cookies, which I hate because then you are exposed to privacy invasion by everyone and their pets. A more reasonable solution would be to allow third-party cookies only from wordpress.com, if your browser supports it.
Workaround: Have two browsers (say the one bundled with your OS and Firefox/Opera) and enable third party cookies in one of them, then use it only to browse your blog.
As far as I know, this problem can't be solved because that's the way cookies and browsers are supposed to work, and there's only one domain actually hosting the blog and handling authentication (wordpress.com) to begin with. Still, disabling third party cookies is a sensible practice, so I think this caveat should be mentioned somewhere.