I think if people sign in using FBC then asking for a password seems redundant. In the FB process you guys should request the email permission and if they want to get their password email it to them.
When creating my account, with the Flash 10.1 RC4 build, in Chromium 6.0.432 on OSX, I clicked the FB connect button, immediately get a Flash player crash message, no FB window comes up, and it never registers.
I ended up switching to Safari 5 to complete registration.