Not to reduce their work, but this article on UPnP "hacking" [site's currently not loading very reliably] uses a lot of words to make a small point. So here it is in shorter form:
Many (most) routers use UPnP for configuration, which uses SOAP over HTTP.
Despite there being an autodiscovery phase to UPnP that involves non-HTTP packets, you can guess a router's IP anyway and you don't need to do autodiscovery to run commands.
Flash lets you set arbitrary HTTP headers and POST to arbitrary hosts. This is standard XSRF -- the POSTing could be done with DHTML, so Flash is just needed to set the SOAP header.
Therefore, malicious Flash can run port-opening commands on your router.
Opening ports doesn't require a password (since software like Skype wants to be able to do it). They claim you can also change the DNS server or admin credentials, which seems to me like it ought to need a password, but maybe they're relying on people leaving default passwords.