I honestly think this base_path thing is a disaster... I am seriously thinking about sticking with beta 4 until a solution is found, because it freaks beginner-coders like me out :-(
Sounds like you shouldn't be using the betas then.
The problem that I have is that when I add it as Ber suggested, all my static links don't work when my site is in a subfolder such as www.mydomain.com/mysite instead of at the root level, www.mydomain.com.
I fail to see how that is an issue - your base_url would change both times to the correct value. If your site is in www.mydomain.com, then your $base_url would be "http://www.mydomain.com". If your site was in a subdirectory, presumably you'd change the value of your settings.php file, and that'd turn your base_url into http://www.mydomain.com/sub.
Where's the actual problem? What links, exactly, aren't working for you? Where is there an online demo so we can see what you're talking about?