Rich,
You shouldn't need to wait, but it never hurts to do so. The v6.1.1 release is planned for Friday, but we're still testing, so it may be delayed until next week.
Either way, whenever you upgrade any extension, not just JFBConnect, if you have template overrides, you need to incorporate any changes from the new releases layout files into your overrides. Otherwise, you'll either a) run into errors where old code from your override won't work or b) new features won't work since your old file won't know to call them.
To be clear, the 'fix' in the 6.1.1 release will prevent Fatal Errors. However, if you still have an old template override, your Forgot Username and Forgot Password links will not be visible. You'll need to upgrade your override to use the new layout files to use the new features in the new release. We'll just be avoiding the fatal error situation that some users are experiencing.
That's just how upgrades work if you keep an older version of a file around.
I hope that helps explain,
Alex